The hp-problem for groups with certain central factors cyclic

Joseph A. Gallian

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

The hp-problem for groups with certain central factors cyclic

Joseph A. Gallian

Mathematics & Statistics

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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 -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.

Original language	English (US)
Pages (from-to)	39-41
Number of pages	3
Journal	Proceedings of the American Mathematical Society
Volume	42
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1974-0325762-8
State	Published - Jan 1974

Keywords

Central series of a finite p-group
Finite p-groups
Hp-problem
Hughes problem

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The hp-problem for groups with certain central factors cyclic

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