On the small squaring and commutativity

L. Brailovsky

doi:10.1112/blms/25.4.330

On the small squaring and commutativity

L. Brailovsky^*

^*Corresponding author for this work

School of Computer Science

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Let G be a group and let k > 2 be an integer, such that (A:2 — 3)(A: — 1) ≮ G /15 if G is finite. Suppose that the condition \AZ\ < k(k+l)/2 + (k-’i)/2 is satisfied by every it-element subset A c G. Then G is abelian. The proof uses the structure of quasi-invariant sets.

Original language	English
Pages (from-to)	330-336
Number of pages	7
Journal	Bulletin of the London Mathematical Society
Volume	25
Issue number	4
DOIs	https://doi.org/10.1112/blms/25.4.330
State	Published - Jul 1993

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title = "On the small squaring and commutativity",

abstract = "Let G be a group and let k > 2 be an integer, such that (A:2 — 3)(A: — 1) ≮ G /15 if G is finite. Suppose that the condition \AZ\ < k(k+l)/2 + (k-{\textquoteright}i)/2 is satisfied by every it-element subset A c G. Then G is abelian. The proof uses the structure of quasi-invariant sets.",

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AB - Let G be a group and let k > 2 be an integer, such that (A:2 — 3)(A: — 1) ≮ G /15 if G is finite. Suppose that the condition \AZ\ < k(k+l)/2 + (k-’i)/2 is satisfied by every it-element subset A c G. Then G is abelian. The proof uses the structure of quasi-invariant sets.

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On the small squaring and commutativity

Abstract

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