ApCoCoA-1:Other1 groups

Higman group

Description

This group has the following representation:

 G = <a,b | a^{2}b^{-6} = (ab^{-1})^{3}ab^{-2}ab^{k}a^{-1}b = 1>

where k is congruent to 3 mod 6.

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 CreateRelationsOther1()
   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^{-6} = aadddddd = 1
   Append(Relations,[[a,a,d,d,d,d,d,d],[1]]);
   
   // add the relation (ab^{-1})^{3}ab^{-2}ab^{k}a^{-1}b = 1 with k = 3
   Append(Relations,[[a,d,a,d,a,d,a,d,d,a,b,b,b,c,b],[1]]);
   Return Relations;
 EndDefine;
 
 Relations:=CreateRelationsOther1();
 GB:=NC.GB(Relations,31,1,100,1000);