Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4584248 | Journal of Algebra | 2015 | 4 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
E. Henke, J. Semeraro,