Memoirs of the American Mathematical Society 1997; 77 pp; softcover Volume: 129 ISBN10: 0821806254 ISBN13: 9780821806258 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 2subgroups 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 2cohomology by means of the LyndonHochschildSerre 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 grouptheoretic 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
