Abstract
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.
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Azarov, D.N. On the Weak \( \pi \)-Potency of Some Groups and Free Products. Sib Math J 61, 953–962 (2020). https://doi.org/10.1134/S0037446620060014
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DOI: https://doi.org/10.1134/S0037446620060014