Virtually free finite-normal-subgroup-free groups are strongly verbally closed

Anton A. Klyachko; Andrey M. Mazhuga; Veronika Yu. Miroshnichenko

doi:10.1016/j.jalgebra.2018.05.028

Virtually free finite-normal-subgroup-free groups are strongly verbally closed

Group Theory 2018-06-26 v3

Authors: Anton A. Klyachko , Andrey M. Mazhuga , Veronika Yu. Miroshnichenko

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Abstract

Any virtually free group $H$ containing no non-trivial finite normal subgroup (e.g., the infinite dihedral group) is a retract of any finitely generated group containing $H$ as a verbally closed subgroup.

Keywords

group theory finite group theory

Cite

@article{arxiv.1712.03406,
  title  = {Virtually free finite-normal-subgroup-free groups are strongly verbally closed},
  author = {Anton A. Klyachko and Andrey M. Mazhuga and Veronika Yu. Miroshnichenko},
  journal= {arXiv preprint arXiv:1712.03406},
  year   = {2018}
}

Comments

6 pages. V2: minor corrections. V3: misprint corrections. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm

Virtually free finite-normal-subgroup-free groups are strongly verbally closed

Abstract

Keywords

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