Abstract

Let π be a set of primes. We say that the Sylow π-theorem holds for a finite group G, or G is a Dπ-group, if the maximal π-subgroups of G are conjugate. Obviously, the Sylow π-theorem implies the existence of π-Hall subgroups. In this paper, we give an affirmative answer to Problem 17.44, (b), in the Kourovka notebook: namely, we prove that in a Dπ-group an overgroup of a π-Hall subgroup is always a Dπ-group.

Original languageEnglish
Pages (from-to)309-335
Number of pages27
JournalSbornik Mathematics
Volume211
Issue number3
DOIs
Publication statusPublished - Mar 2020

Keywords

  • Dπ-group
  • Finite group
  • Group of lie type
  • Maximal subgroup
  • π-hall subgroup

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