A Characteristic Subgroup for Fusion Systems
نویسندگان
چکیده
As a counterpart for the prime 2 to Glauberman’s ZJ-theorem, Stellmacher proves that any nontrivial 2-group S has a nontrivial characteristic subgroup W (S) with the following property. For any finite Σ4-free group G, with S a Sylow 2-subgroup of G and with O2(G) self-centralizing, the subgroup W (S) is normal in G. We generalize Stellmacher’s result to fusion systems. A similar construction of W (S) can be done for odd primes and gives rise to a Glauberman functor.
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تاریخ انتشار 2008