Nilpotent residual of fixed points
de Melo, Emerson · Lima, Aline de Souza · Shumyatsky, Pavel
Original · EN
Let q be a prime and A a finite q-group of exponent q acting by automorphisms on a finite q'-group G. Assume that A has order at least q³. We show that if γ∞ (CG(a)) has order at most m for any a ∈ A#, then the order of γ∞ (G) is bounded solely in terms of m and q. If γ∞ (CG(a)) has rank at most r for any a ∈ A#, then the rank of γ∞ (G) is bounded solely in terms of r and q.
English translation
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