Vol. 112, No. 2, 1984

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ISSN: 0030-8730
The calculation of an invariant for Tor

Brian Donald Wick

Vol. 112 (1984), No. 2, 445–450
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 pλ Ext(Z(p),G∕pλG)∕pλ+1 Ext(Z(p),G∕pλG) 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
Authors
Brian Donald Wick