منابع مشابه
Generation of polycyclic groups
Polycyclic groups are one of the best understood class of groups. For example most of the decision problems are decidable in this class, see [7]. It seems surprising therefore that it is still an open problem whether there exists an algorithm which finds d(G) for any polycyclic group G (given by say a set of generators and relations). This is unknown even in the case when G is virtually abelian...
متن کاملOn Ordered Polycyclic Groups
It has been asserted that any (full) order on a torsion-free, finitely generated, nilpotent group is defined by some F-basis of G and that the group of o-automorphisms of such a group is itself a group of the same kind: Examples provided herein demonstrate that both of these assertions are false; however, it is proved that the group of o-automorphisms of an ordered, polycyclic group is nilpoten...
متن کاملDecidable Properties of Polycyclic Groups
The classical decision problems of group theory were formulated with finitely presented groups in mind. In this generality they are all known to be algorithmically insoluble (Novikov, Boone, Adian and Rabin). The recent work of Kharlampovich and Baumslag, Gildenhuys and Strebel [9,2] has established similar negative results within the category of finitely presented soluble groups. The picture i...
متن کاملUniform Growth of Polycyclic Groups
The Milnor-Wolf Theorem characterizes the finitely generated solvable groups which have exponential growth; a finitely generated solvable group has exponential growth iff it is not virtually nilpotent. Wolf showed that a finitely generated nilpotent by finite group has polynomial growth; then extended this by proving that polycyclic groups which are not virtually nilpotent have expontial growth...
متن کاملAutomorphism groups of polycyclic-by-finite groups and arithmetic groups
We show that the outer automorphism group of a polycyclic-by-finite group is an arithmetic group. This result follows from a detailed structural analysis of the automorphism groups of such groups. We use an extended version of the theory of the algebraic hull functor initiated by Mostow. We thus make applicable refined methods from the theory of algebraic and arithmetic groups. We also construc...
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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2009
ISSN: 1433-5883,1435-4446
DOI: 10.1515/jgt.2008.098