Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-05T12:56:45.509Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)