Difference between revisions of "Group Examples"
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ftp://apcocoa.org/pub/symbolic_data | ftp://apcocoa.org/pub/symbolic_data | ||
| − | === | + | === Non-abelian Groups === |
| − | ==== Baumslag groups ==== | + | ==== <div id="Baumslag_groups">Baumslag groups</div> ==== |
The [ftp://apcocoa.org/pub/symbolic_data/non_commutative/baumslag.coc Baumslag] (respectively Baumslag-Solitar) groups are examples of two-generator one-relator groups. | The [ftp://apcocoa.org/pub/symbolic_data/non_commutative/baumslag.coc Baumslag] (respectively Baumslag-Solitar) groups are examples of two-generator one-relator groups. | ||
| − | The first variante of this group has the presentation <a, b | a^m = b^n = 1 > | + | The first variante of this group has the presentation |
| − | + | <a, b | a^m = b^n = 1 > | |
| − | The second variante of this group (the Baumslag-Solitar group) has the presentation <a, b | b*a^m = a^n*b> | + | where m, n are natural numbers. The second variante of this group (the Baumslag-Solitar group) has the presentation |
| − | + | <a, b | b*a^m = a^n*b> | |
| + | where m, n are natural numbers. [[:ApCoCoA:Symbolic data Computations#Baumslag_groups|Computations of Baumslag groups]]. | ||
(Reference: ) | (Reference: ) | ||
Revision as of 12:15, 29 May 2013
ftp://apcocoa.org/pub/symbolic_data
Non-abelian Groups
Baumslag groups
The Baumslag (respectively Baumslag-Solitar) groups are examples of two-generator one-relator groups. The first variante of this group has the presentation
<a, b | a^m = b^n = 1 >
where m, n are natural numbers. The second variante of this group (the Baumslag-Solitar group) has the presentation
<a, b | b*a^m = a^n*b>
where m, n are natural numbers. Computations of Baumslag groups.
(Reference: )
Braid groups
For a natural number n the Braid group has n strands and n - 1 generators: g_1, g_2, ... , g_(n - 1) and relations: g_i * g_j = g_j * g_i for |i - j| >= 2 and g_i * g_(i + 1) * g_i = g_(i + 1) * g_i * g_(i + 1) for 1 <= i <= n - 2 Type Braid(n, [DegreeBound, LoopBound]) to calculate the Gröbner base.
Dihedral groups
The Dihedral group of degree n (natural number) has the presentation <a, b | a^2 = b^n = 1, aba = b^-1> Type Dihedral(n, [DegreeBound, LoopBound]) to calculate the Gröbner base.
