Subgroups - If K is a subgroup of H and H is a subgroup of G, is K a subgroup of G? Please justify your answer.
Group Theory - let G be a finite group with K is a normal subgroup of G. If (l K l, [G:K]) =1, prove that K is unique subgroup of G having order l K l.
Sylow groups - a) Let G be a group of order 203. Prove that if H is normal subgroup of order 7 in G then H<=Z(G). Deduce that G is abelian in this case.
b)Let P be a normal Sylow p-subgroup of G and let H be any ...
subgroup problem - show that {(1), (1,2)(3,4), (1,3)(2,4), (1,4)(2,3)} is a subgroup of S4 (Ssub4)