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Generalized Direct Products of Groups and their Application to the Study of Residuality of Free Constructions of Groups

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Algebra and Logic Aims and scope

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 HNN-extension with central associated subgroups to be residually a C-group where C is a root class of groups. In particular, it is proved that an HNN-extension of a solvable group with central associated subgroups is residually solvable.

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Authors and Affiliations

  1. Ivanovo State University, ul. Ermaka 39, Ivanovo, 153025, Russia

    E. V. Sokolov & E. A. Tumanova

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  1. E. V. Sokolov
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  2. E. A. Tumanova
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Correspondence to E. V. Sokolov.

Additional information

Supported by RFBR, project No. 18-31-00187.

Translated from Algebra i Logika, Vol. 58, No. 6, pp. 720-740, November-December, 2019.

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Sokolov, E.V., Tumanova, E.A. Generalized Direct Products of Groups and their Application to the Study of Residuality of Free Constructions of Groups. Algebra Logic 58, 480–493 (2020). https://doi.org/10.1007/s10469-020-09568-x

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  • DOI: https://doi.org/10.1007/s10469-020-09568-x

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