The calculation of an invariant for Tor

Brian Donald Wick

Vol. 112 (1984), No. 2, 445–450

DOI: 10.2140/pjm.1984.112.445

Abstract

Let λ be a limit ordinal such that λ is not cofinal with ω and let G = Tor(A,B) where A and B are reduced p-groups. It is shown that the invariant defined to be the dimension of the Z∕pZ-vector space p^λ Ext(Z(p^∞),G∕p^λG)∕p^λ+1 Ext(Z(p^∞),G∕p^λG) is zero. If A, B and Tor(A,B) are three totally projective p-groups then either A or B must be the direct sum of countable p-groups.

Mathematical Subject Classification 2000

Primary: 20K10

Secondary: 20K40

Milestones

Received: 9 November 1981

Published: 1 June 1984