The reduction theorem for relatively maximal subgroups

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Let be a class of finite groups closed under taking subgroups, homomorphic images and extensions. It is known that if A is a normal subgroup of a finite group G then the image of an-maximal subgroup H of G in G/A is not, in general,-maximal in G/A. We say that the reduction-Theorem holds for a finite group A if, for every finite group G that is an extension of A (i.e. contains A as a normal subgroup), the number of conjugacy classes of-maximal subgroups in G and G/A is the same. The reduction-Theorem for A implies that HA/A is-maximal in G/A for every extension G of A and every-maximal subgroup H of G. In this paper, we prove that the reduction-Theorem holds for A if and only if all-maximal subgroups of A are conjugate in A and classify the finite groups with this property in terms of composition factors.

Original languageEnglish
Article number2150001
JournalBulletin of Mathematical Sciences
DOIs
Publication statusE-pub ahead of print - 16 Jan 2021

Keywords

  • -maximal subgroup
  • -submaximal subgroup
  • Complete class
  • finite simple group

OECD FOS+WOS

  • 1.01 MATHEMATICS

Fingerprint

Dive into the research topics of 'The reduction theorem for relatively maximal subgroups'. Together they form a unique fingerprint.

Cite this