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Yet another Freiheitssatz: Mating finite groups with locally indicable ones

Part of: Special aspects of infinite or finite groups Low-dimensional topology

Published online by Cambridge University Press:  14 November 2022

Anton A. Klyachko  and
Mikhail A. Mikheenko
Anton A. Klyachko*
Affiliation:
Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, MSU, Moscow 119991, Russia Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia
Mikhail A. Mikheenko
Affiliation:
Faculty of Mechanics and Mathematics, Moscow State University, Leninskie Gory, MSU, Moscow 119991, Russia Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia
*
*Corresponding author. E-mail: klyachko@mech.math.msu.su
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Abstract

The main result includes as special cases on the one hand, the Gerstenhaber–Rothaus theorem (1962) and its generalisation due to Nitsche and Thom (2022) and, on the other hand, the Brodskii–Howie–Short theorem (1980–1984) generalising Magnus’s Freiheitssatz (1930).

Keywords

equations over groupsFreiheitssatz

MSC classification

Primary: 20F70: Algebraic geometry over groups; equations over groups
Secondary: 20F65: Geometric group theory 57M07: Topological methods in group theory
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 65 , Issue 2 , May 2023 , pp. 337 - 344
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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Footnotes

*

Definitions, examples, and properties of hyperlinear (= Connes-embeddable) groups can be found, e.g., in [36]; we note only that the class of hyperlinear groups contains all finite group and their free products (possibly, even all group are hyperlinear – this is a well-known open question).

This work was supported by the Russian Science Foundation, project no. 22-11-00075.

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