ApCoCoA-1:VonDyck groups

Von Dyck groups

Description

 D(l,m,n) = <x,y | x^{l} = y^{m} = (xy)^{n} = 1>

(Reference: not found yet)

Computation

 /*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 CreateRelationsDicyclic()
   Relations:=[];
    
   // add the relation a^{n} = b^2
   Append(Relations, [[a^(MEMORY.N)], [b,b]]);
   
   // add the relation a^{2n} = 1
   Append(Relations, [[a^(2*MEMORY.N)], [1]]);
   
   // add the relation b^{-1}ab = a^{-1}
   Append(Relations, [[b^(3),a,b],[a^(2*MEMORY.N-1)]]);
   Return Relations;
 EndDefine;
 
 Relations:=CreateRelationsDicyclic();
 Relations;
 GB:=NC.GB(Relations);
 GB;