The Spread of Almost Simple Classical Groups

By: Scott Harper

Write A Review

Paperback | 26 May 2021

At a Glance

Paperback
164 Pages

Dimensions(cm)
23.5 x 15.5 x 0.89

Paperback

RRP $84.99

$68.75

19%OFF

or 4 interest-free payments of $17.19 with

Ships in 10 to 15 business days

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.

Industry Reviews

"The monograph is essentially dedicated to experts in the field and provides a detailed analysis of the spread of the groups, as part of a wider current research project." (Enrico Jabara, zbMATH 1510.20001, 2023)

"The purposes of the monograph are twofold. Firstly, it provides an introduction to the almost simple classical groups for a broad audience, including graduate students new to the area. Secondly, for the experts in the field, it provides a detailed analysis of the spread of these groups, as part of a wider current research project." (Stefan Kohl, Mathematical Reviews, May, 2022)

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $89.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.