On a conjecture of Karrass and Solitar

2013/03/29 by Benjamin Steinberg, Steinberg, Benjamin
Mathematics · #20E06 #20F65 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20E06 #msc:20F65

paper · pdf · doi:10.48550/arxiv.1303.7279

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

arxiv created 2013/11/07 · arxiv updated 2013/11/08

Abstract

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

Related

• A simple proof of a theorem of Karrass and Solitar
• A new proof of a theorem of Ivanov and Schupp
• Fixed Subgroups of Endomorphisms of Free Products
• On pairs of finitely generated subgroups in free groups
• Kurosh rank of intersections of subgroups of free products of orderable groups