A block theoretic analogue of a theorem of Glauberman and Thompson

Kessar, R. & Linckelmann, M. (2003). A block theoretic analogue of a theorem of Glauberman and Thompson. Proceedings of the American Mathematical Society, 131(1), pp. 35-40.

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Abstract

If p is an odd prime, G a finite group and P a Sylow-p-subgroup of G, a theorem of Glauberman and Thompson states that G is p-nilpotent if and only if NG(Z(J(P))) is p-nilpotent, where J(P) is the Thompson subgroup of P generated by all abelian subgroups of P of maximal order. Following a suggestion of G. R. Robinson, we prove a block-theoretic analogue of this theorem.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: School of Engineering & Mathematical Sciences > Department of Mathematical Science
URI: http://openaccess.city.ac.uk/id/eprint/1893

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