The finite irreducible linear 2-groups of degree 4
Author(s)
Bibliographic Information
The finite irreducible linear 2-groups of degree 4
（Memoirs of the American Mathematical Society, no. 613）
American Mathematical Society, 1997
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Note
"September 1997, volume 129, number 613 (first of 4 numbers)"
Includes bibliographical references (p. 76-77)
Description and Table of Contents
Description
This memoir contains a complete classification of the finite irreducible 2-subgroups of $GL(4, {\mathbb C})$. Specifically, the author provides a parametrized list of representatives for the conjugacy classes of such groups, where each representative is defined by a 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.It's features include: a complete classification of a class of $p$-groups; a first step towards extending presently available databases for use in proposed 'soluble quotient algorithms'; and, groups presented explicitly; may be used to test conjectures or to serve generally as a resource in group-theoretic computations.
Table of Contents
Introduction Preliminaries The isomorphism question The case $T=V_4$ The case $T=C$ The case $T=D$ Full solutions Schur indices References.
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