The hughes conjecture and groups with absolutely regular subgroups or ECF-subgroups

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Abstract

Let G be a finite p-group and Hp(G) the subgroup generated by the elements of G of order different from p. Hughes conjectured that if formula presented then formula presented. Although the conjecture is not true for all G, it is shown here that if G has a subgroup L such that formula presented or an ECF-subgroup L with formula presented then G satisfies the Hughes conjecture.

Original languageEnglish (US)
Pages (from-to)315-318
Number of pages4
JournalProceedings of the American Mathematical Society
Volume49
Issue number2
DOIs
StatePublished - Jun 1975

Keywords

  • Absolutely regular groups
  • ECF-groups
  • Finite p-groups
  • Hp-problem
  • Hughes conjecture

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