The main result of the paper is the following theorem. Let q be a prime and A an elementary abelian group of order q^3. Suppose that A acts coprimely on a profinite group G and assume that C_G(a) is locally nilpotent for each a∈A#. Then the group G is locally nilpotent.
Profinite groups and the fixed points of coprime automorphisms / Acciarri, C; Shumyatsky, P. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - 452:(2016), pp. 188-195. [10.1016/j.jalgebra.2016.01.010]
Profinite groups and the fixed points of coprime automorphisms
ACCIARRI C;
2016
Abstract
The main result of the paper is the following theorem. Let q be a prime and A an elementary abelian group of order q^3. Suppose that A acts coprimely on a profinite group G and assume that C_G(a) is locally nilpotent for each a∈A#. Then the group G is locally nilpotent.
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