arXiv subjects
Publications and source records attributed to D. I. Moldavanskii.
A criterion for the HNN-extension of a finite p-group to be residually a finite p-group is obtained and based on this criterion the sufficient condition for residuality a finite p-group of HNN-extension with arbitrary base group is proved. Then these results are applied to give for groups from two classes of one-relator groups the necessary and sufficient condition to be residually a finite p-group.
A class of one-relator groups such that every group in the class is determined by a triple of integers and is an HNN-extension of some Baumslag -- Solitar group is considered. A criterion for two groups in this class to be isomorphic and criterion for two non-isomorphic groups to be a homomorphic image of each other are obtained. This result leads to a negative answer to the question 3.33 from "Kourovka Notebook".
Conjugacy separability of any group of the class of one-relator groups given by the presentation $ $ ($m,n>1$) is proven.
The description of the automorphism group of group $ $ ($m,n>1$) in terms of generators and defining relations is given. This result is applied to prove that any normal automorphism of every such group is inner.