"Source: Text/Group/GrpGPC.text";
"Line: 1774";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpGPC.text, line: 1774
// Example: H81E9 ()
print "Example: H81E9";
ei := GetEchoInput();
SetEchoInput(true);
F<a,b,c,d,e> := FreeGroup(5);
rels := [ b^a = b*e^2, b^(a^-1) = b*e^-2, d^c = d*e^3,
          d^(c^-1) = d*e^-3 ];
G<a,b,c,d,e> := quo< GrpGPC: F | rels >;
IsNilpotent(G);
assert $1;
H1 := sub<G|a>;          
H2 := sub<G|b>;
H3 := sub<G|c>;
H4 := sub<G|d>;
H5 := sub<G|e>;

C12 := CommutatorSubgroup(H1, H2);
{@ G!x : x in PCGenerators(C12) @};
C12 subset H5;
assert $1;
C34 := CommutatorSubgroup(H3, H4);
{@ G!x : x in PCGenerators(C34) @};
C34 subset H5;
assert $1;
C := C12 meet C34;
{@ G!x : x in PCGenerators(C) @};
IsCyclic(C); 
assert $1;
IsCentral(G, C);
assert $1;
SetEchoInput(ei);
