Direct products and elementary equivalence of polycyclic-by-finite groups
نویسندگان
چکیده
منابع مشابه
ELEMENTARY EQUIVALENCE OF PROFINITE GROUPS by
There are many examples of non-isomorphic pairs of finitely generated abstract groups that are elementarily equivalent. We show that the situation in the category of profinite groups is different: If two finitely generated profinite groups are elementarily equivalent (as abstract groups), then they are isomorphic. The proof applies a result of Nikolov and Segal which in turn relies on the class...
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...
متن کاملAlgorithms for Polycyclic-by-finite Groups Algorithms for Polycyclic-by-finite Groups Table of Contents
OF THE DISSERTATION Algorithms for Polycyclic-by-Finite Groups by Gretchen Ostheimer Dissertation Director: Professor Charles C. Sims Let R be a number eld. We present several algorithms for working with polycyclicbynite subgroups of GL(n;R). Let G be a subgroup of GL(n;R) given by a nite generating set of matrices. We describe an algorithm for deciding whether or not G is polycyclic-bynite. Fo...
متن کاملElementary Equivalence of Profinite Groups
There are many examples of non-isomorphic pairs of finitely generated abstract groups that are elementarily equivalent. We show that the situation in the category of profinite groups is different: If two finitely generated profinite groups are elementarily equivalent (as abstract groups), then they are isomorphic. The proof applies a result of Nikolov and Segal which in turn relies on the class...
متن کاملElementary Equivalence and Profinite Completions: a Characterization of Finitely Generated Abelian-by-finite Groups
In this paper, we show that any finitely generated abelian-byfinite group is an elementary submodel of its profinite completion. It follows that two finitely generated abelian-by-finite groups are elementarily equivalent if and only if they have the same finite images. We give an example of two finitely generated abelian-by-finite groups G, H which satisfy these properties while G x Z and H x Z...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2014
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2014.07.006