Algebra and Logic

, Volume 41, Issue 3, pp 187–206

The Dπ-Property in a Class of Finite Groups

  • D. O. Revin

DOI: 10.1023/A:1016029025936

Cite this article as:
Revin, D.O. Algebra and Logic (2002) 41: 187. doi:10.1023/A:1016029025936


A finite group G is a Dπ-group for some set π of primes if maximal π-subgroups of G are all conjugate. Assume that every non-Abelian composition factor of the Dπ-group G is isomorphic either to an alternating group, or to one of the sporadic groups, or to a simple group of Lie type over a field whose characteristic belongs to π. We prove that an extension of G by an arbitrary Dπ-group and every normal subgroup of G are Dπ-groups. This gives partial answers to Questions 3.62 and 13.33 in the “Kourovka Notebook.” Also, we describe all Dπ-groups whose composition factors are isomorphic to alternating, sporadic, and Lie-type groups whose characteristics belong to π. And bring to a close the description of Hall subgroups in sporadic groups, initiated by F. Gross.

Dπ-groupalternating groupsporadic groupsimple group of Lie typeHall subgroup

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • D. O. Revin
    • 1
  1. 1.Novosibirsk State UniversityRussia