The 𝐻_{𝑝}-problem for groups with certain central factors cyclic

Gallian, Joseph A.

doi:10.1090/S0002-9939-1974-0325762-8

The $H_{p}$-problem for groups with certain central factors cyclic
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Proc. Amer. Math. Soc. 42 (1974), 39-41 Request permission

Abstract:

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 p-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.

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A problem in group theory

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