Unit:
Τομέας Άλγεβρας ΓεωμετρίαςLibrary of the School of Science
Author:
Παραμαντζόγλου Παναγιώτης
Dissertation committee:
Δημήτριος Βάρσος Καθηγητής (επιβλέπων), Ευάγγελος Ράπτης Καθηγητής, Ολυμπία Ταλέλλη Καθηγήτρια
Original Title:
Περί της τομής πεπερασμένα παραγόμενων υποομάδων μίας ομάδας- Η ιδιότητα του Howson σε HNN-επεκτάσεις και Αμαλγάματα
Translated title:
On the intersection of finitely generated subgroups of a group (The Howson property in HNN-extensions and Amalgamated free products)
Summary:
A group G has the Howson property (or is a Howson group) if the intersection of
any two finitely generated subgroups of G is again finitely generated. This
property is «natural» for some classes of groups, such as finite groups and
polycyclic groups. Firstly Howson showed that free groups have this property.
Also free products of Howson groups are Howson. Sufficient conditions, which
ensure that an amalgamated free product or an HNN-extension of Howson groups is
again a Howson group are given by Burns and Cohen. The target of this
dissertation is to characterize the amalgamated free products or the
HNN-extensions of polycyclic groups concerning the Howson property. We give
conditions for ΗΝΝ-extensions of finitely generated abelian groups and for
amalgamated free products of finitely generated nilpotent groups. There are
some others partial results. Interesting open problems dirives from this
dissertation.
Keywords:
Howson property, HNN-extensions, Amalgamated free products, Polycyclic groups, Free groups
