"Source: Text/Group/GrpFP.text";
"Line: 4867";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Group/GrpFP.text, line: 4867
// Example: H80E35 ()
print "Example: H80E35";
ei := GetEchoInput();
SetEchoInput(true);
G<a,b> := DihedralFPGroup(0);
H := sub< G | a*b, a^10 >;
Index(G, H);
assert $1 eq 10;
RT, transmap := Transversal(G, H);
RT;
transmap;
LT := {@ x^-1 : x in RT @};
LT;
ct := CosetTable(G, H);
forall(culprit){ i : i in [1..Index(G, H)]
                   | ct(1, RT[i]) eq i};
assert $1;
action := func< r, g | RT[ct(Index(RT, r), g)] >;
action(Id(G), b); 
action(a^-4, a*b);
SetEchoInput(ei);
