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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$42
Individual Members: US$25.20
Institutional Members: US$33.60
Order Code: MEMO/129/613
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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

Readership

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

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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