This article is cited in 12 papers

Generalized direct products of groups and their application to the study of residuality of free constructions of groups

E. V. Sokolov, E. A. Tumanova

Ivanovo State University

Abstract: We introduce the construction of a generalized direct product associated with a graph of groups and prove two sufficient conditions for its existence. These results are applied to obtain some sufficient conditions for an $\mathrm{HNN}$-extension with central associated subgroups to be residually a $\mathcal{C}$-group where $\mathcal{C}$ is a root class of groups. In particular, it is proved that an $\mathrm{HNN}$-extension of a solvable group with central associated subgroups is residually solvable.

Keywords: generalized direct product, generalized free product, $\mathrm{HNN}$-extension, residual finiteness, residual $p$-finiteness, residual solvability, root-class residuality.

UDC: 512.543

Received: 12.02.2019
Revised: 12.02.2020

DOI: 10.33048/alglog.2019.58.604

 English version: Algebra and Logic, 2020, 58:6, 480–493

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