On the Weak \( \pi \) -Potency of Some Groups and Free Products

Сибирский математический журнал

article

D. N. Azarov¹ 

[1] Ivanovo State University

关键词: potent group;    residually finite group;    soluble minimax group;    generalized free product;   

DOI  :  10.1134/S0037446620060014

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

Let $ \pi $ be a set of primes. A group  $ G $ is weakly $ \pi $ -potent if $ G $ is residually finite and, for each element  $ x $ of infinite order in  $ G $ , there is a positive integer  $ m $ such that, for every positive $ \pi $ -integer  $ n $ , there exists a homomorphism of $ G $ onto a finite group which sends  $ x $ to an element of order  $ mn $ . We obtain a few results about weak $ \pi $ -potency for some groups and generalized free products.

【 授权许可】

CC BY