Let G be a group and Hp(G) the subgroup generated by the elements of G of order different from p. Hughes conjectured that if G>Hp(G)>1, then \G:Hp(G)\=p. In this paper it is shown that if G is a finite -group and certain central factors of G are cyclic or if the normal subgroups of G of a certain order are two generated, then the Hughes conjecture is true for G.
- Central series of a finite p-group
- Finite p-groups
- Hughes problem