1. A Property Equivalent to n-Permutability for Infinite Groups
- Author
-
Alireza Abdollahi, Aliakbar Mohammadi Hassanabadi, and Bijan Taeri
- Subjects
Combinatorics ,Discrete mathematics ,Permutation ,Algebra and Number Theory ,Infinite group ,Integer ,Group (mathematics) ,Permutable prime ,Mathematics - Abstract
Let n be an integer greater than 1. A group G is said to be n -permutable whenever for every n -tuple ( x 1 ,…, x n ) of elements of G there exists a non-identity permutation σ of {1,…, n } such that x 1 ··· x n = x σ(1) ··· x σ( n ) . In this paper we prove that an infinite group G is n -permutable if and only if for every n infinite subsets X 1 ,…, X n of G there exists a non-identity permutation σ on {1,…, n } such that X 1 ··· X n ∪ X σ(1) ··· X σ( n ) ≠ ∅ .
- Published
- 1999
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