On subgroups of free Burnside groups of large odd exponent

2002/10/13 by S. V. Ivanov, Ivanov, S. V.
Mathematics · #20E07 #20F05 #20F50 #Advanced Topology and Set Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras #math.GR #msc:20E07 #msc:20F05 #msc:20F50

paper · pdf · doi:10.48550/arxiv.math/0210191

5 pages

arxiv created 2002/10/13 · openalex publication_date 2002/10/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every noncyclic subgroup of a free m-generator Burnside group B(m,n) of odd exponent n ≫ 1 contains a subgroup H isomorphic to a free Burnside group B(∞,n) of exponent n and countably infinite rank such that for every normal subgroup K of H the normal closure ^B(m,n) of K in B(m,n) meets H in K. This implies that every noncyclic subgroup of B(m,n) is SQ-universal in the class of groups of exponent n.

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