**Memoirs of the American Mathematical Society**

1997;
77 pp;
Softcover

MSC: Primary 20;

Print ISBN: 978-0-8218-0625-8

Product Code: MEMO/129/613

List Price: $45.00

Individual Member Price: $27.00

**Electronic ISBN: 978-1-4704-0198-6
Product Code: MEMO/129/613.E**

List Price: $45.00

Individual Member Price: $27.00

# The Finite Irreducible Linear 2-Groups of Degree 4

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*D. L. Flannery*

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.