Almost-free groups in varieties with torsion

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Abstract

Let V be a variety of groups. A group G is said to be almost V-free if every subgroup of G that can be generated by fewer elements than the cardinality of G is contained in a V-free subgroup. It is shown in this paper that if V is a variety in which there is a finite non-abelian simple group, then there are for each positive integer n, 2אn almost V-free groups of cardinality אn.

Original languageEnglish
Pages (from-to)174-178
Number of pages5
JournalJournal of Algebra
Volume108
Issue number1
DOIs
Publication statusPublished - 1 Jan 1987
Externally publishedYes

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