Cohomology, Fusion and a P-nilpotency Criterion
نویسنده
چکیده
Let G be a finite group, p a fix prime and P a Sylow p-subgroup of G. In this short note we prove that if p is odd, G is p-nilpotent if and only if P controls fusion of cyclic groups of order p. For the case p = 2, we show that G is p-nilpotent if and only if P controls fusion of cyclic groups of order 2 and 4.
منابع مشابه
Tate's and Yoshida's theorems on control of transfer for fusion systems
We prove analogues of results of Tate and Yoshida on control of transfer for fusion systems. This requires the notions of p-group residuals and transfer maps in cohomology for fusion systems. As a corollary we obtain a p-nilpotency criterion due to Tate.
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