On w-maximal groups

2010/03/31 by Jon González‐Sánchez, Jon Gonzalez-Sanchez, Gonzalez-Sanchez, Jon +2
Mathematics · #20F99 #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #Limits and Structures in Graph Theory #math.GR #msc:20F99

paper · pdf · doi:10.48550/arxiv.1003.6048

15 pages

arxiv created 2010/03/31 · openalex publication_date 2010/03/31 · arxiv updated 2010/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let w = w(x₁,..., x_n) be a word, i.e. an element of the free group F =<x₁,...,x_n> on n generators x₁,..., x_n. The verbal subgroup w(G) of a group G is the subgroup generated by the set \w (g₁,...,g_n)^{± 1} | g_i ∈ G, 1≤ i≤ n \ of all w-values in G. We say that a (finite) group G is w-maximal if |G:w(G)|> |H:w(H)| for all proper subgroups H of G and that G is hereditarily w-maximal if every subgroup of G is w-maximal. In this text we study w-maximal and hereditarily w-maximal (finite) groups.

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