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THE CONSISTENCY OF HOLT'S CONJECTURES ON COHOMOLOGICAL DIMENSION OF LOCALLY FINITE GROUPS

Published online by Cambridge University Press:  01 February 1997

P. H. KROPHOLLER  and
S. THOMAS
P. H. KROPHOLLER
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London E1 4NS, UK
S. THOMAS
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903, USA
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Abstract

Let G be a locally finite group of cardinality ℵn where n is a natural number. Let π(G) be the set of primes p for which G has an element of order p. In [5], Holt conjectures that if k is a finite field with char k ∉ π(G) then

(1) G has cohomological dimension n+1 over k;

(2) Hn+1(G, kG) has cardinality 2ℵn;

(3) Hi(G, kG) = 0 for 0 [les ] i [les ] n.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 55 , Issue 1 , February 1997 , pp. 76 - 86
Copyright
The London Mathematical Society 1997

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