Nilpotent residual and Fitting subgroup of fixed points in finite groups

2019/03/02 by de Melo, Emerson
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1903.01440

Abstract

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_∞ (C_G(a)) has order at most m for any a ∈ A^#, then the order of γ_∞ (G) is bounded solely in terms of m. If the Fitting subgroup of C_G(a) has index at most m for any a ∈ A^#, then the second Fitting subgroup of G has index bounded solely in terms of m.

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