Article ID Journal Published Year Pages File Type
4584248 Journal of Algebra 2015 4 Pages PDF
Abstract

Glauberman's Z⁎Z⁎-theorem and analogous statements for odd primes show that, for any prime p and any finite group G with Sylow p-subgroup S  , the centre of G/Op′(G)G/Op′(G) is determined by the fusion system FS(G)FS(G). Building on these results we show a statement that seems a priori more general: For any normal subgroup H of G   with Op′(H)=1Op′(H)=1, the centralizer CS(H)CS(H) is expressed in terms of the fusion system FS(G)FS(G) and its normal subsystem induced by H.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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