The mod–2 cohomology ring of the third conway group is cohen–macaulay
King, Simon A
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King, Simon A; Green, David; Ellis, Graham (2011). The mod–2 cohomology ring of the third conway group is cohen–macaulay. Algebraic & Geometric Topology 11 (2), 719-734
By explicit machine computation we obtain the mod-2 cohomology ring of the third Conway group Co(3). It is Cohen-Macaulay, has dimension 4, and is detected on the maximal elementary abelian 2-subgroups.