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Journal of the London Mathematical Society 1995 51(2):259-278; doi:10.1112/jlms/51.2.259
© 1995 by London Mathematical Society
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© The London Mathematical Society

The Cohomology of the Sylow 2-Subgroup of J2

John Maginnis

Mathematics Department, Kansas State University Manhattan, Kansas 66506, USA

Received 19 April 1993. Revision received 19 October 1993.

The Hall-Janko-Wales group J2 is one of the twenty-six sporadic finite simple groups. The cohomology of its Sylow 2-subgroup SJ is computed, an important step in calculating the mod 2 cohomology of J2. The spectral sequence corresponding to the central extension for SJ is described and shown to collapse at the eighth page. The group SJ contains two subgroups Formula (the central product of a dihedral and a quaternionic group) and 22+4 (the Sylow 2-subgroup of the matrix group PSL3(F4)) which detect the cohomology of SJ. The cohomology relations for the subgroup 22+4 are computed.


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