𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Finite extensions of A-solvable abelian groups

✍ Scribed by Ulrich Albrecht

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
137 KB
Volume
158
Category
Article
ISSN
0022-4049

No coin nor oath required. For personal study only.

✦ Synopsis

An abelian group G is almost A-solvable if the natural map Γ‚G: Hom(A; G) E(A) A β†’ G is a quasi-isomorphism. Two strongly indecomposable torsion-free abelian groups A and B of ΓΏnite rank are quasi-isomorphic if and only if the classes of almost A-solvable and almost B-solvable groups coincide. Homological properties of almost A-solvable groups are described, and several examples are given. In particular, there exists a torsion-free almost A-solvable group which is not quasi-isomorphic to an A-solvable group.

πŸ“œ SIMILAR VOLUMES

On Preservation of Stability for Finite
On Preservation of Stability for Finite Extensions of Abelian Groups
✍ Frieder Haug πŸ“‚ Article πŸ“… 1994 πŸ› John Wiley and Sons 🌐 English βš– 778 KB

## Abstract We characterize preservation of superstability and ω‐stability for finite extensions of abelian groups and reduce the general case to the case of __p__‐groups. In particular we study finite extensions of divisible abelian groups. We prove that superstable abelian‐by‐finite groups have o