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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.
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- Research Article
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- © 2019 Australian Mathematical Publishing Association Inc.
Footnotes
This work was supported by the Engineering and Physical Sciences Research Council.