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The Finite Irreducible Linear 2-Groups of Degree 4
D. L. Flannery, University of Canberra, ACT, Australia
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Memoirs of the American Mathematical Society
1997; 77 pp; softcover
Volume: 129
ISBN-10: 0-8218-0625-4
ISBN-13: 978-0-8218-0625-8
List Price: US$45 Individual Members: US$27
Institutional Members: US\$36
Order Code: MEMO/129/613

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.

Features:

• A complete classification of a class of $$p$$-groups
• A first step towards extending presently available databases for use in proposed "soluble quotient algorithms"
• Groups presented explicitly; may be used to test conjectures or to serve generally as a resource in group-theoretic computations

Graduate students and research mathematicians interested in group theory and representation theory.

• The case $$T=V_4$$
• The case $$T=C$$
• The case $$T=D$$