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INTERSECTIONS OF SUBGROUPS IN VIRTUALLY FREE GROUPS AND VIRTUALLY FREE PRODUCTS
Part of
- Structure and classification of infinite or finite groups
- Graph theory
ANTON A. KLYACHKO, ANASTASIA N. PONFILENKO
Journal:

Bulletin of the Australian Mathematical Society / Volume 101 / Issue 2 / April 2020

Published online by Cambridge University Press:

18 July 2019, pp. 266-271

Print publication:

April 2020
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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 $\text{rank}(A\cap B)-1\leq n\cdot (\text{rank}(A)-1)\cdot (\text{rank}(B)-1)$. In addition, we obtain a virtually-free-product analogue of this result.