Given an integer n≠0,1, let B_n be the variety of n-Bell groups defined by the law [x^n,y]=[x,y^n], and let B*_n be the class of all groups G in which, for any infinite subsets X and Y of G, there exist elements x in X and y in Y such that [x^n,y]=[x,y^n]. We prove that every infinite B*_n-group G is n-Bell in the following cases: G is finitely generated and locally graded; G is locally soluble; G is locally graded and |n| or |n-1| is equal to 2^ap^b (where p is a prime, and a, b are non-negative integers). We also show that every infinite B*_4 -group is a 4-Bell group.
Locally graded groups with a Bell condition on infinite subsets
TORTORA, ANTONIO
2009
Abstract
Given an integer n≠0,1, let B_n be the variety of n-Bell groups defined by the law [x^n,y]=[x,y^n], and let B*_n be the class of all groups G in which, for any infinite subsets X and Y of G, there exist elements x in X and y in Y such that [x^n,y]=[x,y^n]. We prove that every infinite B*_n-group G is n-Bell in the following cases: G is finitely generated and locally graded; G is locally soluble; G is locally graded and |n| or |n-1| is equal to 2^ap^b (where p is a prime, and a, b are non-negative integers). We also show that every infinite B*_4 -group is a 4-Bell group.File in questo prodotto:
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