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.
76-86
Kropholler, P.H.
0a2b4a66-9f0d-4c52-8541-3e4b2214b9f4
Thomas, S.
0f83004b-179e-4b71-8374-25345d0e9dad
February 1997
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), .
(doi:10.1112/S0024610796003225).
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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Published date: February 1997
Organisations:
Mathematical Sciences
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Local EPrints ID: 349598
URI: http://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: 15 Mar 2024 03:46
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S. Thomas
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