Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
Please make all selections above before adding to cart
Copy To Clipboard
Successfully Copied!
Black Box Classical Groups

William M. Kantor University of Oregon, Eugene, OR
Ákos Seress Ohio State University, Columbus, OH
Available Formats:
Electronic ISBN: 978-1-4704-0299-0
Product Code: MEMO/149/708.E
List Price: $66.00 MAA Member Price:$59.40
AMS Member Price: $39.60 Click above image for expanded view Black Box Classical Groups William M. Kantor University of Oregon, Eugene, OR Ákos Seress Ohio State University, Columbus, OH Available Formats:  Electronic ISBN: 978-1-4704-0299-0 Product Code: MEMO/149/708.E  List Price:$66.00 MAA Member Price: $59.40 AMS Member Price:$39.60
• Book Details

Memoirs of the American Mathematical Society
Volume: 1492001; 168 pp
MSC: Primary 20; Secondary 68;

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.

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

• Chapters
• 1. Introduction
• 2. Preliminaries
• 3. Special linear groups: PSL($d, q$)
• 4. Orthogonal groups: $P\Omega ^\epsilon (d, q)$
• 5. Symplectic groups: $\mathrm {PSp}(2m, q)$
• 6. Unitary groups: $\mathrm {PSU}(d, q)$
• 7. Proofs of Theorems 1.1 and 1.1′, and of Corollaries 1.2–1.4
• 8. Permutation group algorithms
• 9. Concluding remarks
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1492001; 168 pp
MSC: Primary 20; Secondary 68;

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.

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

• Chapters
• 1. Introduction
• 2. Preliminaries
• 3. Special linear groups: PSL($d, q$)
• 4. Orthogonal groups: $P\Omega ^\epsilon (d, q)$
• 5. Symplectic groups: $\mathrm {PSp}(2m, q)$
• 6. Unitary groups: $\mathrm {PSU}(d, q)$
• 7. Proofs of Theorems 1.1 and 1.1′, and of Corollaries 1.2–1.4
• 8. Permutation group algorithms
• 9. Concluding remarks
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.