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INTERSECTIONS OF SUBGROUPS IN VIRTUALLY FREE GROUPS AND VIRTUALLY FREE PRODUCTS

Published online by Cambridge University Press:  18 July 2019

ANTON A. KLYACHKO*
Affiliation:
Faculty of Mechanics and Mathematics, Moscow State University, Leninskie gory, Moscow 119991, Russia email [email protected]
ANASTASIA N. PONFILENKO
Affiliation:
Faculty of Mechanics and Mathematics, Moscow State University, Leninskie gory, Moscow 119991, Russia email [email protected]

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

Type
Research Article
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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Footnotes

The work of the first author was supported by the Russian Foundation for Basic Research, project no. 19-01-00591.

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