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SUBGROUPS WITH NO ABELIAN COMPOSITION FACTORS ARE NOT DISTINGUISHED
Published online by Cambridge University Press: 13 September 2019
Abstract
Given a finite group $G$, define the minimal degree
$\unicode[STIX]{x1D707}(G)$ of
$G$ to be the least
$n$ such that
$G$ embeds into
$S_{n}$. We call
$G$ exceptional if there is some
$N\unlhd G$ with
$\unicode[STIX]{x1D707}(G/N)>\unicode[STIX]{x1D707}(G)$, in which case we call
$N$ distinguished. We prove here that a subgroup with no abelian composition factors is not distinguished.
MSC classification
- Type
- Research Article
- Information
- Copyright
- © 2019 Australian Mathematical Publishing Association Inc.
Footnotes
This work was supported by the Engineering and Physical Sciences Research Council.