On subgroups of free Burnside groups of large odd exponent

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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 〈K〉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.

Original languageEnglish (US)
Pages (from-to)299-304
Number of pages6
JournalIllinois Journal of Mathematics
Volume47
Issue number1-2
DOIs
StatePublished - 2003

ASJC Scopus subject areas

  • Mathematics(all)

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