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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The $ H\sb{p}$-problem for groups with certain central factors cyclic


Author: Joseph A. Gallian
Journal: Proc. Amer. Math. Soc. 42 (1974), 39-41
MSC: Primary 20D15
DOI: https://doi.org/10.1090/S0002-9939-1974-0325762-8
MathSciNet review: 0325762
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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 $ \vert G:Hp(G)\vert = 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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DOI: https://doi.org/10.1090/S0002-9939-1974-0325762-8
Keywords: Finite p-groups, $ {H_p}$-problem, Hughes problem, central series of a finite p-group
Article copyright: © Copyright 1974 American Mathematical Society