Combinatorial conditions forcing commutativity of an infinite group

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Abstract

We show that the function f(n)=⌈(5n2-3n-2)/6⌉ is the best possible squaring bound for infinite abelian groups. That is, if G is an infinite group and k is an integer ≥ 2, such that the condition, |K2| ≤ f(k), holds for every k-element subset K ⊆ G then G is abelian. Moreover, f(n) is the "maximal" integer valued function with this property. A characterization of central-by-finite groups appears in the proof.

Original languageEnglish
Pages (from-to)394-400
Number of pages7
JournalJournal of Algebra
Volume165
Issue number2
DOIs
StatePublished - 15 Apr 1994

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