 
Summary: JOURNAL OF
PURE AND
APPLIEDALGEBRA
Journal of Pure and Applied Algebra 110 (1996) 109112
On a conjecture of Moore
E. Aljadeff"** J. Cornickb, Y. Ginosara, P.H. Kropholler"
BDepartment of Mathematics, Technion, Israel Inst. of Technology, Haifa, 32000, Israel
"Centre de Recerca Matematica, Institut D'Estudis Catalans, Apartat 50, EO8193 Bellatewa, Spain
`School of Mathematical Sciences, Queen Maly and Weseeld College, Mile End road, London Ei 4NS, UK
Communicated by CA. Weibel; received 3 January 1995
1. Introduction
We address a conjecture of J.C. Moore which concerns a criterion for a module
over a group ring to be projective. Throughout, G denotes a group, H is a subgroup of
finite index and R denotes a ring. The primary object is to study modules over the
group ring RG. In [3]. Chouinard records the following.
Moore's Conjecture. Suppose thatfor all x E G\H, either there is an integer n such that
1 # x" E H or x has Jinite order invertible in R. Then every RGmodule M which is
projective over RH is also projective over RG.
This can be regarded as a generalization of Serre's Theorem that every torsionfree
group of finite virtual cohomological dimension has finite cohomological dimension
