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

E. V. Sokolov ; E. A. Tumanova

Algebra i logika, Tome 58 (2019) no. 6, pp. 720-740.

Résumé

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.

Détail

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

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