The Mod-2 Cohomology Ring of the Third Conway Group is Cohen-Macaulay
Simon A. King, David J. Green, Graham Ellis
TL;DR
This paper computes the mod-2 cohomology ring of the third Conway group Co_3, revealing it is Cohen-Macaulay with dimension 4 and detectable on maximal elementary abelian 2-subgroups, using explicit machine computation.
Contribution
It provides the first explicit computation of the mod-2 cohomology ring of Co_3, demonstrating its Cohen-Macaulay property and detection on specific subgroups.
Findings
Cohomology ring of Co_3 is Cohen-Macaulay
The cohomology ring has dimension 4
Detection occurs on maximal elementary abelian 2-subgroups
Abstract
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.
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