Engel-like conditions in fixed points of automorphisms of profinite\n groups

2019/02/21 by Cristina Acciarri, Acciarri, Cristina, Danilo Silveira +1
Computer Science · Mathematics · #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1902.08612

openalex publication_date 2019/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let q be a prime and A an elementary abelian q-group acting as a\ncoprime group of automorphisms on a profinite group G. We show that if A is\nof order q² and some power of each element in C_G(a) is Engel in G for\nany a\∈ A ^#, then G is locally virtually nilpotent. Assuming that A\nis of order q³ we prove that if some power of each element in C_G(a) is\nEngel in C_G(a) for any a\∈ A ^#, then G is locally virtually\nnilpotent. Some analogues consequences of quantitative nature for finite groups\nare also obtained.\n

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