Geodesic
Generalized direct products of groups and their application to the study of residuality of free constructions of groups
Algebra i logika, Tome 58 (2019) no. 6, pp. 720-740

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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, residual finiteness, residual $p$-finiteness, residual solvability, root-class residuality.
Mots-clés : $\mathrm{HNN}$-extension 
@article{AL_2019_58_6_a3,
     author = {E. V. Sokolov and E. A. Tumanova},
     title = {Generalized direct products of groups and their application to the study of residuality of free constructions of groups},
     journal = {Algebra i logika},
     pages = {720--740},
     publisher = {mathdoc},
     volume = {58},
     number = {6},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2019_58_6_a3/}
}
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E. V. Sokolov; E. A. Tumanova. Generalized direct products of groups and their application to the study of residuality of free constructions of groups. Algebra i logika, Tome 58 (2019) no. 6, pp. 720-740. http://geodesic.mathdoc.fr/item/AL_2019_58_6_a3/