On the rank of the intersection of free subgroups in virtually free groups

2013/01/14 by Alexander Zakharov, Zakharov, Alexander
Mathematics · #20E06 #20E08 #20F65 #Advanced Operator Algebra Research #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:20E06 #msc:20E08 #msc:20F65

paper · pdf · doi:10.48550/arxiv.1301.3115

10 pages; main results strengthened, references updated, proof of Theorem 1 simplified

openalex publication_date 2013/01/14 · arxiv created 2013/11/02 · arxiv updated 2013/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove an estimate for the rank of the intersection of free subgroups in virtually free groups, which is analogous to the Hanna Neumann inequality for subgroups in a free group and to the S.V. Ivanov estimate for subgroups in free products of groups. We also prove a more general estimate for the rank of the intersection of free subgroups in the fundamental group of a finite graph of groups with finite edge groups.

Related

• Kurosh rank of intersections of subgroups of free products of orderable groups
• Achievable ranks of intersections of finitely generated free groups
• The Hanna Neumann Conjecture and the rank of the join
• Intersecting free subgroups in free amalgamated products of two groups with normal finite amalgamated subgroup
• On a conjecture of Imrich and Müller