Black box classical groups / William M. Kantor, Ákos Seress.

Format:

Book

Author/Creator:

Kantor, W. M. (William M.), 1944- author.

Seress, Ákos, 1958- author.

Series:

Memoirs of the American Mathematical Society ; no. 708.

Memoirs of the American Mathematical Society, 0065-9266 ; number 708

Language:

English

Subjects (All):

Permutation groups.

Matrix groups.

Algorithms.

Physical Description:

1 online resource (183 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2001]

Language Note:

English

Summary:

If a black box simple group is known to be isomorphic to a classical group over a field of known characteristic, a Las Vegas algorithm is used to produce an explicit isomorphism. The proof relies on the geometry of the classical groups rather than on difficult group-theoretic background. This algorithm has applications to matrix group questions and to nearly linear time algorithms for permutation groups. In particular, we upgrade all known nearly linear time Monte Carlo permutation group algorithms to nearly linear Las Vegas algorithms when the input group has no composition factor isomorphic to an exceptional group of Lie type or a 3-dimensional unitary group.

Contents:

Intro

Contents

1 Introduction

2 Preliminaries

3 Special linear groups: PSL(d,q)

4 Orthogonal groups: PΩ[sup(ε)] (d,q)

5 Symplectic groups: PS[sub(p)](2m,q)

6 Unitary groups: PSU(d,q)

7 Proofs of Theorems 1.1 and 1.1', and of Corollaries 1.2-1.4

8 Permutation group algorithms

9 Concluding remarks

References.

Notes:

Description based upon print version of record.

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0299-8