On the Howson property of descending HNN-extensions of groups

2012/08/15 by Moldavanskii David, David, Moldavanskii
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1208.3075

Translation from Russian of the paper published in Chebyshevskii sbornik (Publishers of Tula State Pedagogic University), Vol.11, issue 3(35), 2010, 103 - 110

arxiv created 2012/08/15 · arxiv updated 2012/08/16

Abstract

A group G is said to have the Howson property (or to be a Howson group) if the intersection of any two finitely generated subgroups of G is finitely generated subgroup. It is proved that descending HNN-extension is not a Howson group under some assumptions satisfied by the base group of HNN-extension. In particular, a result of the paper joined with a Burns - Brunner result (received in 1979) implies that any descending HNN-extension of non-cyclic free group does not have the Howson property.

Related

• Howson groups which are not strongly Howson
• A non-Hopfian ascending HNN-extension of a finitely presented Hopfian group
• A criterion for HNN extensions of finite p-groups to be residually p
• Some characterizations of Howson PC-groups
• Failure of the finitely generated intersection property for ascending HNN extensions of free groups