Intersections of subgroups in virtually free groups and virtually free products

Abstract

This note contains a (short) proof of the following generalisation of the Friedman--Mineyev theorem (earlier known as the Hanna Neumann conjecture): if $A$ and $B$ are nontrivial free subgroups of a virtually free group containing a free subgroup of index $n$, then $rank(A\cap B)-1⩽n\cdot (rank(A)-1)\cdot (rank(B)-1)$. In addition, we obtain a virtually-free-product analogue of this result.

3 pages. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm . V.2: minor corrections and refinements