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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10.1090/S0002-9939-1974-0325762-8

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title = "The hp-problem for groups with certain central factors cyclic",

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 \textbackslash{}G:Hp(G)\textbackslash{}=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.",

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AU - Gallian, Joseph A.

PY - 1974/1

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N2 - 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.

AB - 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.

KW - Central series of a finite p-group

KW - Finite p-groups

KW - Hp-problem

KW - Hughes problem

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DO - 10.1090/S0002-9939-1974-0325762-8

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EP - 41

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 1

ER -

The hp-problem for groups with certain central factors cyclic

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