92g:20083 20J06 20D08

Adem, Alejandro ^{(}1-STF^{)}; Maginnis, John ^{(}1-MI^{)};

Milgram, R. James ^{(}1-STF^{)}

The geometry and cohomology of the Mathieu group M_{12}. J. Algebra 139 (1991), no. 1, 90–133. This paper is devoted to the calculation of the cohomology ring of the sporadic Mathieu group M_{12} with mod 2 coefficients. The ring turns out to be Cohen-Macaulay, with Poincare series p(H^{∗}(M_{12}, F_{2}), t) = (1 + t^{3})^{2}/(1 − t^{2})(1 − t^{3})(1 − t^{4}). The method is based on using the action of M_{12} on the poset of elementary abelian 2-subgroups to reduce to the calculation of the cohomology of a pair of 2-local subgroups intersecting in a Sylow 2-subgroup. David Benson (4-OX)

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