Premium
The Cohomology of the Sylow 2‐Subgroup of J 2
Author(s) -
Maginnis John
Publication year - 1995
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/51.2.259
Subject(s) - sylow theorems , mathematics , group cohomology , dihedral group , cohomology , equivariant cohomology , omega and agemo subgroup , group (periodic table) , combinatorics , pure mathematics , finite group , physics , torsion subgroup , abelian group , elementary abelian group , quantum mechanics
The Hall‐Janko‐Wales group J 2 is one of the twenty‐six sporadic finite simple groups. The cohomology of its Sylow 2‐subgroup S J is computed, an important step in calculating the mod 2 cohomology of J 2 . The spectral sequence corresponding to the central extension for S J is described and shown to collapse at the eighth page. The group S J contains two subgroups 2 _ 1 + 4(the central product of a dihedral and a quaternionic group) and 2 2+4 (the Sylow 2‐subgroup of the matrix group PSL 3 ( 4 )) which detect the cohomology of S J . The cohomology relations for the subgroup 2 2+4 are computed.