User contributions
From ApCoCoAWiki
- 16:00, 18 September 2013 diff hist +653 ApCoCoA-1:GroupsToCheck
- 15:59, 18 September 2013 diff hist +1,084 N ApCoCoA-1:Other13 groups New page: === <div id="Other13_groups">Other groups</div> === ==== Description ==== This group has the following finite representation: G = <x,y | x^2 = xy^{...
- 15:59, 18 September 2013 diff hist -1 Group Examples →Other groups
- 15:59, 18 September 2013 diff hist +1,084 N ApCoCoA-1:Other13" groups New page: === <div id="Other13_groups">Other groups</div> === ==== Description ==== This group has the following finite representation: G = <x,y | x^2 = xy^{... current
- 15:52, 18 September 2013 diff hist -15 ApCoCoA-1:Other11 groups
- 15:52, 18 September 2013 diff hist -15 ApCoCoA-1:Other12 groups
- 15:51, 18 September 2013 diff hist +1,284 N ApCoCoA-1:Other12 groups New page: === <div id="Other12_groups">Other groups</div> === ==== Description ==== This group has the following finite representation: G = <x,t | tx^{a}t^{-...
- 15:50, 18 September 2013 diff hist -1 Group Examples →Other groups
- 15:49, 18 September 2013 diff hist +1,284 N ApCoCoA-1:Other12" groups New page: === <div id="Other12_groups">Other groups</div> === ==== Description ==== This group has the following finite representation: G = <x,t | tx^{a}t^{-... current
- 15:39, 18 September 2013 diff hist +1 ApCoCoA-1:Other11 groups
- 15:38, 18 September 2013 diff hist -2 Group Examples →Other groups
- 15:38, 18 September 2013 diff hist +513 Group Examples →Other groups
- 15:22, 18 September 2013 diff hist +1,341 N ApCoCoA-1:Other11 groups New page: === <div id="Other5_groups">Other groups</div> === ==== Description ==== This group has the following finite representation: G = <x,t | xt^{r} = tx...
- 15:13, 18 September 2013 diff hist +23 ApCoCoA-1:Other5 groups
- 15:11, 18 September 2013 diff hist +251 Group Examples →Other groups
- 15:00, 18 September 2013 diff hist +69 Group Examples
- 14:59, 18 September 2013 diff hist +43 Group Examples
- 14:56, 18 September 2013 diff hist +868 Group Examples →Other groups
- 14:38, 18 September 2013 diff hist +1,026 N ApCoCoA-1:Other7 groups New page: === <div id="Other7_groups">Other groups</div> === ==== Description ==== The next group has the order |G| = 9216 and the following finite representa...
- 14:34, 18 September 2013 diff hist 0 ApCoCoA-1:Other5 groups
- 14:32, 18 September 2013 diff hist 0 Group Examples →Other groups
- 14:31, 18 September 2013 diff hist +1 Group Examples →Other groups
- 14:30, 18 September 2013 diff hist +239 Group Examples →Other groups
- 14:06, 18 September 2013 diff hist 0 ApCoCoA-1:Other5 groups
- 14:05, 18 September 2013 diff hist +1,873 N ApCoCoA-1:Other5 groups New page: === <div id="Other5_groups">Other groups</div> === ==== Description ==== The first group, denoted by G, has an order |G| = 4224 and can be represent...
- 13:43, 18 September 2013 diff hist +811 N ApCoCoA-1:Other4 groups New page: === <div id="Other4_groups">Other groups</div> === ==== Description ==== This group has the following representation: G = <a,b | a^2 = b^3 = (abab...
- 13:42, 18 September 2013 diff hist +19 ApCoCoA-1:GroupsToCheck
- 13:40, 18 September 2013 diff hist -1 ApCoCoA-1:Other2 groups
- 11:56, 18 September 2013 diff hist +212 ApCoCoA-1:GroupsToCheck
- 11:54, 18 September 2013 diff hist +1,745 N ApCoCoA-1:Other2 groups New page: === <div id="Other2_groups">Other groups</div> === ==== Description ==== The first group is called Rosenberger-Monster and is the largest finite ge...
- 11:38, 18 September 2013 diff hist -1 ApCoCoA-1:Other1 groups
- 11:38, 18 September 2013 diff hist +1,064 N ApCoCoA-1:Other1 groups New page: === <div id="Higman_groups">Higman group</div> === ==== Description ==== This group has the following representation: G = <a,b | a^{2}b^{-6} = (ab...
- 11:35, 18 September 2013 diff hist +257 Group Examples →Other groups
- 09:02, 18 September 2013 diff hist +1,681 N ApCoCoA-1:Triangle groups New page: === <div id="Triangle groups">Triangle groups</div> === ==== Description ==== For integers l,m,n greater than 1 the Triangle groups have can be d...
- 08:40, 13 September 2013 diff hist -135 Group Examples →Alternating groups
- 08:39, 13 September 2013 diff hist +434 ApCoCoA-1:GroupsToCheck
- 08:36, 13 September 2013 diff hist +1,148 Group Examples
- 08:05, 13 September 2013 diff hist +1,127 N ApCoCoA-1:Hecke groups New page: === <div id="Hecke_groups">Hecke groups</div> === ==== Description ==== The Hecke groups has the following representation: H(lambda_q) = <x,y | x^...
- 08:03, 13 September 2013 diff hist -21 Group Examples →Hecke groups
- 07:48, 13 September 2013 diff hist +1,300 N ApCoCoA-1:Alternating groups New page: === <div id="Alternating_groups">Alternating groups</div> === ==== Description ==== The alternating groups is the group of all even permutatio...
- 10:03, 10 September 2013 diff hist +300 ApCoCoA-1:GroupsToCheck
- 08:15, 10 September 2013 diff hist +66 Group Examples →Triangle groups
- 07:16, 10 September 2013 diff hist +867 N ApCoCoA-1:Modular group New page: === <div id="Modular_group">Modular group</div> === ==== Description ==== The Modular group has the following representation: PSL(2,Z) = <a,b | a...
- 07:08, 10 September 2013 diff hist 0 ApCoCoA-1:SpecialLinear group
- 07:08, 10 September 2013 diff hist +1 ApCoCoA-1:SpecialLinear group
- 07:06, 10 September 2013 diff hist +1,114 N ApCoCoA-1:SpecialLinear group New page: === <div id="SpecialLinear_group">SpecialLinear group</div> === ==== Description ==== The special linear group over Z is the group of all n x...
- 06:59, 10 September 2013 diff hist +1,180 N ApCoCoA-1:Quaternion group New page: === <div id="Quaternion_group">Quaternion group</div> === ==== Description ==== This particular group is non-abelian with the order 8. The Quate...
- 06:58, 10 September 2013 diff hist +2,524 N ApCoCoA-1:Tits group New page: === <div id="Tits_group">Tits group</div> === ==== Description ==== The Tits group was found by Jacques Tits in 1964. It is a finite simple group and ...
- 06:58, 10 September 2013 diff hist +446 ApCoCoA-1:GroupsToCheck
- 06:57, 10 September 2013 diff hist +783 N ApCoCoA-1:Ikosaeder group New page: === <div id="Ikosaeder group">Ikosaeder group</div> === ==== Description ==== The Ikosaeder group has the following representation: I = <a,b |...
- 06:57, 10 September 2013 diff hist +900 N ApCoCoA-1:Oktaeder group New page: === <div id="Oktaeder group">Oktaeder group</div> === ==== Description ==== The Oktaeder group is a subgroup of the symmetric group. Like the Tetr...
- 06:57, 10 September 2013 diff hist +954 N ApCoCoA-1:Tetraeder group New page: === <div id="Tetraeder group">Tetraeder group</div> === ==== Description ==== The Tetraeder group is isomorphic to the alternating group A_4. Geo...
- 06:56, 10 September 2013 diff hist -97 ApCoCoA-1:Symmetric groups
- 06:49, 10 September 2013 diff hist +1,688 N ApCoCoA-1:Symmetric groups New page: === <div id="Symmetric_groups">Symmetric groups</div> === ==== Description ==== The elements of the symmetric group S_n are all permutations of ...
- 06:47, 10 September 2013 diff hist -1 ApCoCoA-1:Lamplighter group
- 13:09, 20 August 2013 diff hist +11 ApCoCoA-1:Heisenberg groups →Description
- 13:08, 20 August 2013 diff hist +63 N File:HeisenbergMatrix.png Used for the definition of Heisenberg groups in "Symbolic Data" current
- 10:16, 20 August 2013 diff hist +1 Group Examples →Alternating groups
- 10:16, 20 August 2013 diff hist +29 Group Examples
- 10:15, 20 August 2013 diff hist +393 Group Examples
- 10:00, 20 August 2013 diff hist +1,782 Group Examples
- 15:16, 19 August 2013 diff hist -230 Group Examples →Quaternion group
- 15:15, 19 August 2013 diff hist +3 Group Examples →Quaternion group
- 15:14, 19 August 2013 diff hist +900 Group Examples
- 14:53, 19 August 2013 diff hist 0 Group Examples →Ikosaeder group
- 14:52, 19 August 2013 diff hist +2 Group Examples →Symmetric groups
- 14:52, 19 August 2013 diff hist 0 Group Examples →Symmetric groups
- 14:51, 19 August 2013 diff hist 0 Group Examples →Symmetric groups
- 14:50, 19 August 2013 diff hist +1,217 Group Examples
- 14:26, 19 August 2013 diff hist -3 Group Examples →Lamplighter group
- 14:14, 19 August 2013 diff hist +181 ApCoCoA-1:GroupsToCheck
- 14:12, 19 August 2013 diff hist -3 ApCoCoA-1:Lamplighter group
- 14:12, 19 August 2013 diff hist +23 ApCoCoA-1:Lamplighter group
- 14:11, 19 August 2013 diff hist +74 ApCoCoA-1:Lamplighter group
- 14:11, 19 August 2013 diff hist +1,549 N ApCoCoA-1:Lamplighter group New page: === <div id="Lamplighter_groups">Lamplighter groups</div> === ==== Description ==== Lamplighter group: G = <a,b | (ab^{n}ab^{-n})^2 = 1> (R...
- 13:57, 19 August 2013 diff hist -1 Group Examples
- 13:57, 19 August 2013 diff hist +1 Group Examples
- 13:56, 19 August 2013 diff hist -4 Group Examples
- 13:56, 19 August 2013 diff hist +241 Group Examples
- 13:47, 19 August 2013 diff hist -53 ApCoCoA-1:OrdinaryTetrahedron groups →Computation
- 13:42, 19 August 2013 diff hist +3 Group Examples
- 13:42, 19 August 2013 diff hist +1 Group Examples
- 13:42, 19 August 2013 diff hist +239 Group Examples
- 13:38, 19 August 2013 diff hist +353 Group Examples
- 13:21, 19 August 2013 diff hist +148 ApCoCoA-1:GroupsToCheck →Back to Symbolic Data
- 13:19, 19 August 2013 diff hist +54 ApCoCoA-1:GroupsToCheck →Back to Symbolic Data
- 13:18, 19 August 2013 diff hist +44 ApCoCoA-1:OrdinaryTetrahedron groups
- 13:18, 19 August 2013 diff hist +2,154 N ApCoCoA-1:OrdinaryTetrahedron groups New page: === <div id="Higman_groups">Higman group</div> === ==== Description ==== An Ordinary Tetrahedron group is a group with a representation of the form ...
- 09:45, 19 August 2013 diff hist -144 Group Examples →Baumslag groups
- 09:43, 19 August 2013 diff hist +280 ApCoCoA-1:GroupsToCheck →Back to Symbolic Data
- 09:40, 19 August 2013 diff hist -1 ApCoCoA-1:Higman groups →Higman group
- 09:39, 19 August 2013 diff hist +1,594 N ApCoCoA-1:Higman groups New page: === <div id="Higman_groups">Higman group</div> === ==== Description ==== The Higman group is an infinite finitely presented group with no non-trivi...
- 09:34, 19 August 2013 diff hist +4 ApCoCoA-1:Heisenberg groups →Computation
- 09:32, 19 August 2013 diff hist +311 ApCoCoA-1:Heisenberg groups →Description
- 09:03, 19 August 2013 diff hist +57 ApCoCoA-1:Heisenberg groups
- 09:03, 19 August 2013 diff hist +1,741 N ApCoCoA-1:Heisenberg groups New page: === <div id="Heisenberg_groups">Heisenberg groups</div> === ==== Description ==== F(n) = <a_{1},...,a_{n} | a_{i}a_{i}^{-1} = a_{i}^{-1}a_{i...
- 09:00, 19 August 2013 diff hist +84 Group Examples →Ordinary tetrahedron groups
- 09:00, 19 August 2013 diff hist +56 Group Examples →Higman group
- 08:59, 19 August 2013 diff hist +65 Group Examples →Heisenberg groups
- 08:56, 19 August 2013 diff hist +2 Group Examples →Ordinary tetrahedon groups
- 08:54, 16 August 2013 diff hist +198 ApCoCoA-1:GroupsToCheck →Back to Symbolic Data
- 08:49, 16 August 2013 diff hist +1,934 N ApCoCoA-1:Fibonacci groups New page: === <div id="Fibonacci_groups">Fibonacci groups</div> === ==== Description ==== Fibonacci groups are related to the inductive definition of the ...
- 08:37, 16 August 2013 diff hist -133 Group Examples →Fibonacci groups
- 08:26, 16 August 2013 diff hist -15 ApCoCoA-1:Free groups →Computation
- 08:19, 16 August 2013 diff hist -63 Group Examples →Heisenberg groups
- 08:19, 16 August 2013 diff hist +63 Group Examples →Fibonacci groups
- 08:19, 16 August 2013 diff hist +62 Group Examples →Heisenberg groups
- 08:18, 16 August 2013 diff hist +37 Group Examples →Fibonacci groups
- 08:15, 16 August 2013 diff hist -1 Group Examples →Free groups
- 08:15, 16 August 2013 diff hist -1 Group Examples →Free abelian groups
- 08:15, 16 August 2013 diff hist -4 Group Examples →Free groups
- 08:15, 16 August 2013 diff hist -4 Group Examples →Free abelian groups
- 08:15, 16 August 2013 diff hist +159 ApCoCoA-1:Free groups →Free groups
- 08:09, 16 August 2013 diff hist +831 N ApCoCoA-1:Free groups New page: === <div id="Free_groups">Free groups</div> === ==== Description ==== F(n) = <a_{1},...,a_{n} | a_{i}a_{i}^{-1} = a_{i}^{-1}a_{i} = 1> (Reference:...
- 08:03, 16 August 2013 diff hist +57 Group Examples →Free groups
- 08:01, 16 August 2013 diff hist -2 ApCoCoA-1:FreeAbelian groups
- 08:01, 16 August 2013 diff hist +1,011 N ApCoCoA-1:FreeAbelian groups New page: === <div id="FreeAbelian_groups">Free abelian groups</div> === ==== Description ==== Every element in a free abelian group can be written in o...
- 07:55, 16 August 2013 diff hist +72 Group Examples →Free abelian groups
- 07:54, 16 August 2013 diff hist -1 Group Examples →von Dyck groups
- 07:53, 16 August 2013 diff hist +48 ApCoCoA-1:GroupsToCheck →Back to Symbolic Data
- 07:53, 16 August 2013 diff hist +248 ApCoCoA-1:VonDyck groups →Von Dyck groups
- 07:52, 16 August 2013 diff hist -166 Group Examples →Braid groups
- 07:51, 16 August 2013 diff hist +1,310 N ApCoCoA-1:Baumslag-Gersten groups New page: === <div id="Baumslag-Gersten_groups">Baumslag groups</div> === ==== Description ==== The Baumslag-Gersten groups have a Dehn function growing fa...
- 07:45, 16 August 2013 diff hist +77 Group Examples →Baumslag groups
- 07:42, 16 August 2013 diff hist -885 ApCoCoA-1:Dicyclic groups →Computation
- 07:36, 16 August 2013 diff hist -15 ApCoCoA-1:Dihedral groups →Computation
- 10:12, 13 August 2013 diff hist +95 ApCoCoA-1:VonDyck groups →Von Dyck groups
- 10:10, 13 August 2013 diff hist +848 N ApCoCoA-1:VonDyck groups New page: === <div id="VonDyck groups">Von Dyck groups</div> === ==== Description ==== D(l,m,n) = <x,y | x^{l} = y^{m} = (xy)^{n} = 1> (Reference: not f...
- 10:08, 13 August 2013 diff hist +7 Group Examples →von Dyck groups
- 10:07, 13 August 2013 diff hist +53 Group Examples →von Dyck groups
- 10:06, 13 August 2013 diff hist +8 Group Examples →Non-abelian Groups
- 10:06, 13 August 2013 diff hist +36 Group Examples →Non-abelian Groups
- 10:05, 13 August 2013 diff hist +6 ApCoCoA-1:GroupsToCheck →Groups to check
- 10:04, 13 August 2013 diff hist +515 ApCoCoA-1:GroupsToCheck
- 10:00, 13 August 2013 diff hist +6 ApCoCoA-1:GroupsToCheck
- 10:00, 13 August 2013 diff hist +239 N ApCoCoA-1:GroupsToCheck New page: === <div id="GroupsToCheck">Groups to check</div> === ==== Inserted Groups ==== Braid Group Checked: No Notes: -- Cyclic Group Checked: No N...
- 08:18, 13 August 2013 diff hist -268 Group Examples →Dihedral groups
- 08:18, 13 August 2013 diff hist +1,130 N ApCoCoA-1:Dihedral groups New page: === <div id="Dihedral groups">Dihedral groups</div> === ==== Description ==== The dihedral group of degree n is the group of symmetries of a regu...
- 08:16, 13 August 2013 diff hist +66 Group Examples →Dihedral groups
- 08:06, 13 August 2013 diff hist +1 ApCoCoA-1:Dicyclic groups →Description
- 08:06, 13 August 2013 diff hist -34 ApCoCoA-1:Dicyclic groups →Description
- 08:03, 13 August 2013 diff hist +40 ApCoCoA-1:Dicyclic groups →Computation
- 08:02, 13 August 2013 diff hist +601 ApCoCoA-1:Dicyclic groups →Computation
- 07:53, 13 August 2013 diff hist +559 ApCoCoA-1:Dicyclic groups
- 07:50, 13 August 2013 diff hist +17 ApCoCoA-1:Cyclic groups
- 07:49, 13 August 2013 diff hist +4 Group Examples →Dicyclic groups
- 07:49, 13 August 2013 diff hist +57 Group Examples →Dicyclic groups
- 07:49, 13 August 2013 diff hist +824 N ApCoCoA-1:Dicyclic groups New page: →Use the ApCoCoA package ncpoly.: // Number of Dicyclic group (note that the order is 4N) MEMORY.N:=5; Use ZZ/(2)[a,b,c,d]; NC.SetOrdering("LLEX"); Define CreateRe...
- 07:38, 13 August 2013 diff hist +55 ApCoCoA-1:Cyclic groups →Computation
- 07:37, 13 August 2013 diff hist +74 ApCoCoA-1:Braid groups →Computation
- 14:49, 12 August 2013 diff hist -240 ApCoCoA-1:Cyclic groups →Computation
- 14:26, 12 August 2013 diff hist -1 Group Examples →Cyclic groups
- 14:25, 12 August 2013 diff hist +1,155 N ApCoCoA-1:Cyclic groups New page: === <div id="Cyclic_groups">Cyclic groups</div> === ==== Description ==== Every cyclic group is generated by a single element a. If n is finite the...
- 14:09, 12 August 2013 diff hist +58 Group Examples →Cyclic groups
- 14:09, 12 August 2013 diff hist +66 Group Examples →Cyclic groups
- 14:06, 12 August 2013 diff hist +168 ApCoCoA-1:Braid groups →Description
- 13:59, 12 August 2013 diff hist -1 Group Examples →Braid groups
- 13:59, 12 August 2013 diff hist +1 Group Examples →Braid groups
- 13:59, 12 August 2013 diff hist +55 Group Examples →Braid groups
- 13:56, 12 August 2013 diff hist +1,711 N ApCoCoA-1:Braid groups New page: === <div id="Braid_groups">Braid groups</div> === ==== Description ==== The Braid groups have the following presentation. B(n) = <g_{1},...,g_{n-1}...
- 13:32, 12 August 2013 diff hist -1 ApCoCoA-1:Baumslag groups
- 13:31, 12 August 2013 diff hist +1 ApCoCoA-1:Baumslag groups