On finite groups in which commutators are covered by Engel subgroups

2019/01/03 by Pavel Shumyatsky, Shumyatsky, Pavel, Danilo Silveira +1
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1901.01859

9 pages. arXiv admin note: text overlap with arXiv:1702.02899, arXiv:1602.01661

arxiv created 2019/01/03 · arxiv updated 2019/01/08

Abstract

Let m,n be positive integers and w a multilinear commutator word. Assume that G is a finite group having subgroups G₁,…,G_m whose union contains all w-values in G. Assume further that all elements of the subgroups G₁,…,G_m are n-Engel in G. It is shown that the verbal subgroup w(G) is s-Engel for some \m,n,w\-bounded number s.

Citations

• On groups with automorphisms whose fixed points are Engel
• On finite groups with automorphisms whose fixed points are Engel

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