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

[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.

[学科分类] 数学（综合）

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