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The consistency of Holt's conjectures on cohomological dimension of locally finite groups

The consistency of Holt's conjectures on cohomological dimension of locally finite groups
The consistency of Holt's conjectures on cohomological dimension of locally finite groups
Let G be a locally finite group of cardinality ?n where n is a natural number. Let ?(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 ? ?(G) then

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

(2) Hn+1(G, kG) has cardinality 2?n;

(3) Hi(G, kG) = 0 for 0 ? i ? n.
0024-6107
76-86
Kropholler, P.H.
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
Thomas, S.
0f83004b-179e-4b71-8374-25345d0e9dad
Kropholler, P.H.
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
Thomas, S.
0f83004b-179e-4b71-8374-25345d0e9dad

Kropholler, P.H. and Thomas, S. (1997) The consistency of Holt's conjectures on cohomological dimension of locally finite groups. Journal of the London Mathematical Society, 55 (1), 76-86. (doi:10.1112/S0024610796003225).

Record type: Article

Abstract

Let G be a locally finite group of cardinality ?n where n is a natural number. Let ?(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 ? ?(G) then

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

(2) Hn+1(G, kG) has cardinality 2?n;

(3) Hi(G, kG) = 0 for 0 ? i ? n.

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More information

Published date: February 1997
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 349598
URI: https://eprints.soton.ac.uk/id/eprint/349598
ISSN: 0024-6107
PURE UUID: 3d3636fd-7e18-4431-895c-d5df581eafa8

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Date deposited: 09 Apr 2013 15:36
Last modified: 18 Jul 2017 04:40

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