arXiv subjects
Publications and source records attributed to I. B. S. Passi.
Let $1 \to N \to G \to H \to 1$ be an abelian extension. The purpose of this paper is to study the problem of extending automorphisms of $N$ and lifting automorphisms of $H$ to certain automorphisms of $G$.
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.
We present two approaches, one homological and the other simplicial, for the investigation of dimension quotients of groups. The theory is illustrated, in particular, with a conceptual discussion of the fourth and fifth dimension quotients.