Conjugacy of Maximal and Submaximal ν”›-Subgroups

W. Guo, D. O. Revin

Research output: Contribution to journal β€Ί Article β€Ί peer-review

1 Citation (Scopus)

Abstract

Let ν”› be a class of finite groups closed under taking subgroups, homomorphic images, and extensions. Following H. Wielandt, we call a subgroup H of a finite group G a submaximal ν”›-subgroup if there exists an isomorpic embedding Ο•: G β†ͺ G* of the group G into some finite group G* under which GΟ• is subnormal in G* and HΟ• = K ∩GΟ• for some maximal ν”›-subgroup K of G*. We discuss the following question formulated by Wielandt: Is it always the case that all submaximal ν”›-subgroups are conjugate in a finite group G in which all maximal ν”›-subgroups are conjugate? This question strengthens Wielandt’s known problem of closedness for the class of [InlineMediaObject not available: see fulltext.]-groups under extensions, which was solved some time ago. We prove that it is sufficient to answer the question mentioned for the case where G is a simple group.

Original languageEnglish
Pages (from-to)169-181
Number of pages13
JournalAlgebra and Logic
Volume57
Issue number3
DOIs
Publication statusPublished - 1 Jul 2018

Keywords

  • finite group
  • Hall Ο€-subgroup
  • maximal 𝔛-subgroup
  • submaximal 𝔛-subgroup
  • [InlineMediaObject not available: see fulltext.]-property
  • Hall p-subgroup
  • Dpproperty
  • DX-property.
  • maximal X-subgroup
  • HALL SUBGROUPS
  • FINITE-GROUPS
  • submaximal X-subgroup

Fingerprint Dive into the research topics of 'Conjugacy of Maximal and Submaximal ν”›-Subgroups'. Together they form a unique fingerprint.

Cite this