Partitions and sums with inverses in Abelian groups

被引:3
作者
Zelenyuk, Yevhen [1 ]
机构
[1] Univ Witwatersrand, Sch Math, ZA-2050 Wits, South Africa
关键词
partition of a group; finite sums with inverses; absolute resolvability;
D O I
10.1016/j.jcta.2007.05.002
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let G be an Abelian group and let A = {x is an element of G: 2x not equal 0} be infinite. We construct a partition {A(m): m < omega} of A such that whenever (x(n))(n <omega) is a one-to-one sequence in A, g is an element of G and m < omega one has (g + FSI((x(n))(n <omega))) boolean AND A(m) not equal 0, where FSI ((x(n))(n <omega)) = {Sigma(n is an element of F) epsilon(F)(n) x(n) : F is an element of P-f(omega) and epsilon(F)(n) is an element of {1, -1} for all n is an element of F} and P-f(omega) is the set of finite nonempty subseets of omega. (c) 2007 Elsevier Inc. All rights reserved.
引用
收藏
页码:331 / 339
页数:9
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