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Criteria for Commutativity in Large Groups
- Source :
- Canadian Mathematical Bulletin. 41:65-70
- Publication Year :
- 1998
- Publisher :
- Canadian Mathematical Society, 1998.
-
Abstract
- In this paper we prove the following:1.Let m ≥ 2, n ≥ 1 be integers and let G be a group such that (XY)n = (YX)n for all subsets X, Y of size m in G. Thena)G is abelian or a BFC-group of finite exponent bounded by a function of m and n.b)If m ≥ n then G is abelian or |G| is bounded by a function of m and n.2.The only non-abelian group G such that (XY)2 = (YX)2 for all subsets X, Y of size 2 in G is the quaternion group of order 8.3.Let m, n be positive integers and G a group such that for all subsets Xi of size m in G. Then G is n-permutable or |G| is bounded by a function of m and n.
- Subjects :
- Group (mathematics)
General Mathematics
010102 general mathematics
Quaternion group
010103 numerical & computational mathematics
Function (mathematics)
01 natural sciences
Combinatorics
Bounded function
Exponent
Order (group theory)
0101 mathematics
Abelian group
Commutative property
Mathematics
Subjects
Details
- ISSN :
- 14964287 and 00084395
- Volume :
- 41
- Database :
- OpenAIRE
- Journal :
- Canadian Mathematical Bulletin
- Accession number :
- edsair.doi...........ffe6b45896a0d583f0fc6f764fb6b1f7