In 1957 D.R. Hughes published the following problem in group theory. Let G be a group and p a prime. Define Hp(G) to be the subgroup of G generated by all the elements of G which do not have order p . Is the following conjecture true: either Hp(G) = 1, Hp(G) = G , or [G : Hp(G)] = p? This conjecture has become known as the Hughes conjecture. After various classes of groups were shown to satisfy...
