The mod–2 cohomology ring of the third Conway group is Cohen–Macaulay

King, Simon A¹ ; Green, David¹ ; Ellis, Graham²

¹Mathematical Institute, Friedrich-Schiller-Universität Jena, D-07737 Jena, Germany
²School of Maths, Statistics & Applied Maths, National University of Ireland, Galway, University Road, Galway, Ireland

Algebraic and Geometric Topology, Tome 11 (2011) no. 2, pp. 719-734

Résumé

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.

Détail

DOI : 10.2140/agt.2011.11.719

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

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