ApCoCoA-1:Other7 groups
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Description
The next group has the order |G| = 9216 and the following finite representation:
G = <a,b | a^{2}b^{-3} = (ababa^{2}ab^{2})^2 = 1>
Reference
No reference available
Computation
/*Use the ApCoCoA package ncpoly.*/ // a is invers to c and b is invers to d Use ZZ/(2)[a,b,c,d]; NC.SetOrdering("LLEX"); Define CreateRelationsOther7() Relations:=[]; // add the invers relations ac = ca = bd = db = 1 Append(Relations,[[a,c],[1]]); Append(Relations,[[c,a],[1]]); Append(Relations,[[b,d],[1]]); Append(Relations,[[d,b],[1]]); // add the relation a^{2}b^{-3} = 1 Append(Relations,[[a,a,d,d,d],[1]]); // add the relation (ababa^{2}ab^{2})^2= 1 Append(Relations,[[a,b,a,b,a,a,a,b,b,a,b,a,b,a,a,a,b,b],[1]]); Return Relations; EndDefine; Relations:=CreateRelationsOther7(); GB:=NC.GB(Relations,31,1,100,1000);
Example in Symbolic Data Format
<FREEALGEBRA createdAt="2014-01-20" createdBy="strohmeier"> <vars>a,b,c,d</vars> <uptoDeg>14</uptoDeg> <basis> <ncpoly>a*c-1</ncpoly> <ncpoly>c*a-1</ncpoly> <ncpoly>b*d-1</ncpoly> <ncpoly>d*b-1</ncpoly> <ncpoly>a*a*d*d*d-1</ncpoly> <ncpoly>(a*b*a*b*a*a*a*b*b)^2-1</ncpoly> </basis> <Comment>The partial LLex Gb has 199 elements</Comment> <Comment>Other_groups7</Comment> </FREEALGEBRA>