Constraint metric approximations and equations in groups

JOURNAL OF ALGEBRA

卷:516

Article

Arzhantseva, Goulnara¹  Paunescu, Liviu² 

[1] Univ Wien, Fak Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

[2] Romanian Acad, Inst Math, 21 Calea Grivitei St, Bucharest 010702, Romania

关键词: Sofic groups;    Space of sofic representations;    Loeb space;    Metric ultraproducts;    Symmetric groups;    Centralizer;   

DOI  :  10.1016/j.jalgebra.2018.09.007

来源: Elsevier

【 摘 要 】

We introduce notions of a constraint metric approximation and of a constraint stability of a metric approximation. This is done in the language of group equations with coefficients. We give an example of a group which is not constraintly sofic. In building it, we find a sofic representation of free group with trivial commutant among extreme points of the convex structure on the space of sofic representations. We consider the centralizer equation in permutations as an instance of this new general setting. We characterize permutations p is an element of S-k whose centralizer is stable in permutations with respect to the normalized Hamming distance, that is, a permutation which almost centralizes p is near a centralizing permutation. This answers a question of Gorenstein-Sandler-Mills (1962). (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free