Groupe

F := FreeGroup( "a", "b");
 <free group on the generators [ a, b ]> 
Size(F);

infinity

 
G := F/[F.1*F.2/F.1/F.2, F.1^3, F.2^4];
 <fp group on the generators [ a, b ]> 
Size(G);
 12 
GeneratorsOfGroup(G);
 [a,b] 
a := g.1; 
b := g.2;
 a
b		 
AssignGeneratorVariables(G);
//    Idem 
a*a*a*a = a
true 
a in G;
a in F;
true
false		 
a^3 = One(G);
a^3 = One(F) ;
 true
false		 
(a*b)^50;
 (a*b)^50 
SetReducedMultiplication(G);
   
(a*b)^50;
 a^-1*b^2 
IsSubgroupFpGroup(G);
 true 
IsGroupOfFamily(G);
 true 
IsFpGroup(G);
 //    = IsSubgroupFpGroup(G) and IsGroupOfFamily(G)

 

G := FreeGroup(3);
 <free group on the generators [ f1, f2, f3 ]> 
H := CyclicGroup(5);
 <pc group of size 5 with 1 generators> 
IsFpGroup(G);
 false 
AsList(H);
 [ <identity> of ..., f1, f1^2, f1^3, f1^4 ] 
L := FreeGroup("a","b");
AssignGeneratorVariables(L);
G := FactorGroupFpGroupByRels\
 (L, [a*b^3, b*a^3]);
Size(G);
AsList(G);
IsAbelian(G);
<free group on the generators [ a, b ]>
#I Assigned the global variables [ a, b ]

<fp group on the generators [ a, b ]>

8
[ <identity ...>, a, a^-1, b, b^-1, a^2, a*b, a*b^-1 ]
true