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The Finite Irreducible Linear 2-Groups of Degree 4
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This memoir contains a complete classification of the finite irreducible 2-subgroups of GL(4,C). Specifically, the author provides a parametrized list of representatives for the conjugacy classes of such groups, where each representative is defined by generating set of monomial matrices. The problem is treated by a variety of techniques, including elementary character theory, a method for describing Hasse diagrams of submodule lattices, and calculation of 2-cohomology by means of the Lyndon-Hochschild-Serre spectral sequence. Related questions concerning isomorphism between the listed groups, ...
This memoir contains a complete classification of the finite irreducible 2-subgroups of GL(4,C). Specifically, the author provides a parametrized list of representatives for the conjugacy classes of such groups, where each representative is defined by generating set of monomial matrices. The problem is treated by a variety of techniques, including elementary character theory, a method for describing Hasse diagrams of submodule lattices, and calculation of 2-cohomology by means of the Lyndon-Hochschild-Serre spectral sequence. Related questions concerning isomorphism between the listed groups, and Schur indices of their defining characters, are also considered.