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On the Small Squaring and Commutativity
Author(s) -
Brailovsky L.
Publication year - 1993
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/25.4.330
Subject(s) - mathematics , abelian group , commutative property , invariant (physics) , integer (computer science) , combinatorics , discrete mathematics , pure mathematics , mathematical physics , computer science , programming language
Let G be a group and let k > 2 be an integer, such that ( k 2 − 3)( k − 1) < | G |/15 if G is finite. Suppose that the condition | A 2 | ⩽ k ( k + 1)/2 + ( k − 3)/2 is satisfied by every it‐element subset A ⊆ G . Then G is abelian. The proof uses the structure of quasi‐invariant sets.