The spread of almost simple classical groups / Scott Harper.
Harper, Scott (Mathematician), author.
2021
QA174.2
Available Online

Linked e-resources

Linked Resource Online Access
Concurrent users Unlimited
Authorized users Authorized users
Document Delivery Supplied Can lend chapters, not whole ebooks

Details

Title The spread of almost simple classical groups / Scott Harper.
Author Harper, Scott (Mathematician), author.
ISBN 9783030741006 (electronic bk.)
3030741001 (electronic bk.)
9783030741013 (print)
303074101X
3030740994
9783030740993
DOI https://doi.org/10.1007/978-3-030-74100-6
Published Cham, Switzerland : Springer, [2021]
Language English
Description 1 online resource
Other Standard Identifiers 10.1007/978-3-030-74100-6 doi
Call Number QA174.2
Dewey Decimal Classification 512/.2
Summary This monograph studies generating sets of almost simple classical groups, by bounding the spread of these groups. Guralnick and Kantor resolved a 1962 question of Steinberg by proving that in a finite simple group, every nontrivial element belongs to a generating pair. Groups with this property are said to be 3/2-generated. Breuer, Guralnick and Kantor conjectured that a finite group is 3/2-generated if and only if every proper quotient is cyclic. We prove a strong version of this conjecture for almost simple classical groups, by bounding the spread of these groups. This involves analysing the automorphisms, fixed point ratios and subgroup structure of almost simple classical groups, so the first half of this monograph is dedicated to these general topics. In particular, we give a general exposition of Shintani descent. This monograph will interest researchers in group generation, but the opening chapters also serve as a general introduction to the almost simple classical groups.
Bibliography, etc. Note Includes bibliographical references.
Access Note Access limited to authorized users.
Digital File Characteristics text file
PDF
Source of Description Online resource; title from PDF title page (SpringerLink, viewed June 2, 2021).
Series Lecture notes in mathematics (Springer-Verlag) ; 2286. 0075-8434
Available in Other Form Spread of almost simple classical groups.
Linked Resources Online Access
Record Appears in Online Resources > Ebooks
All Resources
Introduction
Preliminaries
Shintani Descent
Fixed Point Ratios
Orthogonal Groups
Unitary Groups.

Browse Subjects

Show more subjects...

Statistics

from
to
Export