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A pair of characteristic subgroups for pushing-up. II

Part of: Structure and classification of infinite or finite groups Representation theory of groups

Published online by Cambridge University Press:  24 October 2012

George Glauberman
George Glauberman*
Affiliation:
Department of Mathematics, University of Chicago, 5734 University Avenue, Chicago, IL 60637-1514, USA (gg@math.uchicago.edu)
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Abstract

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Many problems about local analysis in a finite group G reduce to a special case in which G has a large normal p-subgroup satisfying several restrictions. In 1983, R. Niles and G. Glauberman showed that every finite p-group S of nilpotence class at least 4 must have two characteristic subgroups S1 and S2 such that, whenever S is a Sylow p-subgroup of a group G as above, S1 or S2 is normal in G. In this paper, we prove a similar theorem with a more explicit choice of S1 and S2.

Keywords

Sylow p-subgroupscharacteristic subgroup

MSC classification

Secondary: 20D20: Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure 20E99: None of the above, but in this section
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 1 , February 2013 , pp. 71 - 133
Copyright
Copyright © Edinburgh Mathematical Society 2012

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