test007.in

# Lifted from the Moore & Dickson papers, with B_1, B_2, ... replaced
#   by a, b, ...
# Note that all generators are involutions so that, for example,
#   "(ab)^3" & "aba=bab" are equivalent.

Mess:10000;
Fel;

# S_3, a la Moore

Gr: a,b;
Rel: a^2,b^2, (ab)^3;
End;

# S_3, a la Dickson

Gr: a,b;
Rel: a^2,b^2,  aba=bab;
End;

# S_4, a la Moore

Gr: a,b,c;
Rel: a^2,b^2,c^2, (ab)^3,(bc)^3,  (ac)^2;
End;
Pr;

# S_4/S_3

Gen: a,b;
End;
Pr;

# S_5/S_4, a la Dickson

Gr: a,b,c,d;
Rel: a^2,b^2,c^2,d^2, ac=ca,ad=da,bd=db, aba=bab,bcb=cbc,cdc=dcd;
Gen: a,b,c;
End;
Pr;