The hp-problem for groups with certain central factors cyclic

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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 languageEnglish (US)
Pages (from-to)39-41
Number of pages3
JournalProceedings of the American Mathematical Society
Volume42
Issue number1
DOIs
StatePublished - Jan 1974

Keywords

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

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