Approximations of groups, characterizations of sofic groups, and equations over groups

JOURNAL OF ALGEBRA

卷:477

Article

Glebsky, Lev¹ 

[1] Univ Autonomo San Luis Potosi, Inst Invest Comunicacic Opt, Av Karakorum 1470,Lomas 4a, San Luis Potosi 78210, Mexico

关键词: Sofic groups;    Approximations;    Equations over groups;   

DOI  :  10.1016/j.jalgebra.2016.12.012

来源: Elsevier

【 摘 要 】

We give new characterizations of sofic groups: A group G is sofic if and only if it is a subgroup of a quotient of a direct product of alternating or symmetric groups. A group G is sofic if and only if any system of equations solvable in all alternating groups is solvable over G. The last characterization allows to express soficity of an eltigtentially closed group by\a-sentences. (C)2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free