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

Abstract

According to Mazhuga's theorem, the fundamental group $H$ of any connected 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.

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

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