Volume 11, issue 2 (2011)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
The mod–$2$ cohomology ring of the third Conway group is Cohen–Macaulay

Simon A King, David J Green and Graham Ellis

Algebraic & Geometric Topology 11 (2011) 719–734
Abstract

By explicit machine computation we obtain the mod–2 cohomology ring of the third Conway group Co3. It is Cohen–Macaulay, has dimension 4, and is detected on the maximal elementary abelian 2–subgroups.

Keywords
cohomology of finite groups, group cohomology, third Conway group, stable element, Dickson invariant, simple groups with Cohen–Macaulay cohomology, detection on elementary abelian subgroups
Mathematical Subject Classification 2000
Primary: 20J06
Secondary: 20-04, 20D08
References
Publication
Received: 31 August 2010
Revised: 17 December 2010
Accepted: 22 December 2010
Published: 11 March 2011
Authors
Simon A King
Mathematical Institute
Friedrich-Schiller-Universität Jena
D-07737 Jena
Germany
http://users.minet.uni-jena.de/~king/eindex.html
David J Green
Mathematical Institute
Friedrich-Schiller-Universität Jena
D-07737 Jena
Germany
http://users.minet.uni-jena.de/~green/index-en.php
Graham Ellis
School of Maths, Statistics & Applied Maths
National University of Ireland, Galway
University Road
Galway
Ireland
http://hamilton.nuigalway.ie/