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OVERGROUPS OF PRIMITIVE GROUPS

Part of: Permutation groups Representation theory of groups

Published online by Cambridge University Press:  01 August 2009

MICHAEL ASCHBACHER
MICHAEL ASCHBACHER*
Affiliation:
California Institute of Technology, Pasadena, California 91125, USA (email: asch@its.caltech.edu)
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Abstract

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We give a qualitative description of the set 𝒪G(H) of overgroups in G of primitive subgroups H of finite alternating and symmetric groups G, and particularly of the maximal overgroups. We then show that certain weak restrictions on the lattice 𝒪G(H) impose strong restrictions on H and its overgroup lattice.

Keywords

permutation grouplattice

MSC classification

Secondary: 20B15: Primitive groups 20D30: Series and lattices of subgroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 87 , Issue 1 , August 2009 , pp. 37 - 82
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

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