640 research outputs found
Limits over categories of extensions
We consider limits over categories of extensions and show how certain
well-known functors on the category of groups turn out as such limits. We also
discuss higher (or derived) limits over categories of extensions.Comment: 18 page
Lie Dimension Subrings
We compare, for L a Lie ring over the integers, its lower central series
(\gamma_n(L))_{n>0} and its dimension series defined by \delta_n(L):=L\cap
\varpi^n(L) in the universal enveloping algebra of L. We show that
\gamma_n(L)=\delta_n(L) for all n<4, but give an example showing that they may
differ if n=4. We introduce simplicial methods to describe these results, and
to serve as a possible tool for further study of the dimension series.Comment: Small typos fixed wrt v
Automorphisms of abelian group extensions
Let be an abelian extension. The purpose of this
paper is to study the problem of extending automorphisms of and lifting
automorphisms of to certain automorphisms of .Comment: 11 page
Hyperbolic Unit Groups and Quaternion Algebras
We Classify the rational quadratic extensions K and the finite groups G for
which the group ring R[G] of G over the ring R of integers of K has the
property that the group of units of augmentation 1 of R[G] is hyperbolic. We
also construct units in a non-split quaternion algebra over R.Comment: 15 pages, this work is part of the PHd. Thesis of the third author.
The paper was accepted in Proceedings Mathematical Science
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