On pronormality and strong pronormality of Hall subgroups

M. N. Nesterov

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We study several well-known questions on pronormality and strong pronormality of Hall subgroups. In particular, we exhibit the examples of finite groups (a) having a Hall subgroup not pronormal in its normal closure (this solves Problem 18.32 of The Kourovka Notebook in the negative); (b) having a Hall subgroup pronormal but not strongly pronormal; and (c) that are simple, having a Hall subgroup, and not strongly pronormal (this solves Problem 17.45(b) of The Kourovka Notebook in the negative).

Original languageEnglish
Pages (from-to)128-133
Number of pages6
JournalSiberian Mathematical Journal
Volume58
Issue number1
DOIs
Publication statusPublished - 1 Jan 2017

Keywords

  • finite simple group
  • Hall subgroup
  • pronormal subgroup
  • strongly pronormal subgroup

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