English

On a conjecture of Karrass and Solitar

Group Theory 2013-11-08 v3

Abstract

We settle an old conjecture of Karrass and Solitar by proving that a finitely generated subgroup of a non-trivial free product G=ABG = A\ast B has finite index if and only if it intersects non-trivially each non-trivial normal subgroup of GG. This holds, more generally, for subgroups of finite Kurosh rank.

Keywords

Cite

@article{arxiv.1303.7279,
  title  = {On a conjecture of Karrass and Solitar},
  author = {Benjamin Steinberg},
  journal= {arXiv preprint arXiv:1303.7279},
  year   = {2013}
}

Comments

Changed the intro to reflect comments by G. Arzhantseva on the time frame and history of her work. Referee's corrections implemented