The Klein bottle group is not strongly verbally closed, though awfully close to being so
Group Theory
2021-06-18 v2
Abstract
According to Mazhuga's theorem, the fundamental group of any connected surface, possibly except for the Klein bottle, is a retract of each finitely generated group containing as a verbally closed subgroup. We prove that the Klein bottle group is indeed an exception but has a very close property.
Cite
@article{arxiv.2006.15523,
title = {The Klein bottle group is not strongly verbally closed, though awfully close to being so},
author = {Anton A. Klyachko},
journal= {arXiv preprint arXiv:2006.15523},
year = {2021}
}
Comments
4 pages. V.2: A misprint corrected, thanks to the referee. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm