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ON THE FITTING HEIGHT OF A SOLUBLE GROUP THAT IS GENERATED BY A CONJUGACY CLASS

Published online by Cambridge University Press:  24 March 2003

PAUL FLAVELL
Affiliation:
School of Mathematics and Statistics, University of Birmingham, Birmingham B15 2TT p.j.flavell@bham.ac.uk
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Abstract

Let $G$ be a finite group and suppose that $P$ is a soluble $\{2, 3\}^\prime$ -subgroup of $G$ . The reader will lose only a little by assuming that $P$ is a subgroup of prime order $p > 3$ . Define \[ \Sigma_G(P) = \{A \le G \mid A \hbox{ is soluble and } A = \langle P, P^a\rangle\hbox{ for some }a \in A\}. \] This set is partially ordered by inclusion and we let \[ \Sigma^*_G(P) \] denote the set of maximal members of $\Sigma_G(P)$ .

Type
Notes and Papers
Copyright
The London Mathematical Society, 2002

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