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The Klein bottle group is not strongly verbally closed, though awfully close to being so

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  03 August 2020

Anton A. Klyachko
Anton A. Klyachko*
Affiliation:
Faculty of Mechanics and Mathematics of Moscow State University, Moscow, Leninskie gory, MSU, Russia, 119991
*
e-mail: klyachko@mech.math.msu.su
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Abstract

According to Mazhuga’s theorem, the fundamental group H of anyconnected surface, possibly except for the Klein bottle, is a retract of each finitely generated group containing H as a verbally closed subgroup. We prove that the Klein bottle group is indeed an exception but has a very close property.

Keywords

Verbally closed subgroupssurface groups

MSC classification

Primary: 20F70: Algebraic geometry over groups; equations over groups 20F34: Fundamental groups and their automorphisms 20F16: Solvable groups, supersolvable groups
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 2 , June 2021 , pp. 491 - 497
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Copyright
© Canadian Mathematical Society 2020

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Footnotes

This work was supported by the Russian Foundation for Basic Research, project no. 19-01-00591.

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