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characteristic subgroup

Proceedings of the Edinburgh Mathematical Society (1)

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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
George Glauberman
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 56 / Issue 1 / February 2013

Published online by Cambridge University Press:

24 October 2012, pp. 71-133
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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.