Finite Geometries, Groups, and Computation: Proceedings of the Conference 'Finite Geometries, Groups, and Computation', Pingree Park, Colorado, USA, September 4-9, 2004

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Finite Geometries, Groups, and Computation

Proceedings of the Conference 'Finite Geometries, Groups, and Computation', Pingree Park, Colorado, USA, September 4-9, 2004

Edited by: Alexander Hulpke , Robert Liebler , Tim Penttila and Akos Seress

Language: English

Published/Copyright: 2006

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De Gruyter Proceedings in Mathematics

About this book

This volume is the proceedings of a conference on Finite Geometries, Groups, and Computation that took place on September 4-9, 2004, at Pingree Park, Colorado (a campus of Colorado State University). Not accidentally, the conference coincided with the 60^th birthday of William Kantor, and the topics relate to his major research areas.

Participants were encouraged to explore the deeper interplay between these fields. The survey papers by Kantor, O'Brien, and Penttila should serve to introduce both students and the broader mathematical community to these important topics and some of their connections while the volume as a whole gives an overview of current developments in these fields.

Author / Editor information

Alexander Hulpke and Robert Liebler, Colorado State University, Fort Collins, USA; Tim Penttila, University of Western Australia, Crawley, Australia; Ákos Seress, The Ohio State University, Columbus, USA.

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Frontmatter
i

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Contents
vii

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A reduction algorithm for matrix groups with an extraspecial normal subgroup
1
P. Brooksbank, A. C. Niemeyer and Á. Seress

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A group theoretic approach to (0, 2)-geometries
17
M. R. Brown, C. Tonesi and H. Maldeghem

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Efficient presentations for the Mathieu simple group M22 and its cover
33
M. Conder, G. Havas and C. Ramsay

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On the uniqueness of the unipotent subgroups of some Moufang sets
43
T. Medts, F. Haot, R. Knop and H. Maldeghem

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Symmetric rank 3 designs with regular, elementary abelian, normal subgroups
67
U. Dempwolff

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On minimal subdegrees of finite primitive permutation groups
75
M. Giudici, C. H. Li, C. E. Praeger, Á. Seress and V. Trofimov

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Computing with elation groups
95
G. Havas, C. R. Leedham-Green, E. A. O’Brien and M. C. Slattery

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Finite semifields
103
W. M. Kantor

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Constructions of quasiprimitive two-arc transitive graphs of product action type
115
C. H. Li and Á. Seress

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Symplectic translation planes of even order
125
A. Maschietti

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Structural properties of Hadamard designs
141
E. Merchant

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On projective planes of order less than 32
149
G. E. Moorhouse

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Towards effective algorithms for linear groups
163
E. A. O’Brien

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Finite groups that admit Kantor families
191
S. E. Payne

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Applications of computer algebra to finite geometry
203
T. Penttila

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Finite translation generalized quadrangles: old results, new results, open problems
223
J. A. Thas and K. Thas

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On affine designs and GMW difference sets
237
V. D. Tonchev

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Dimensional dual arcs – a survey
247
S. Yoshiara

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Backmatter
267

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Publishing information

Pages and Images/Illustrations in book

eBook published on:

August 22, 2008

eBook ISBN:

9783110199741

Hardcover published on:

March 15, 2006

Hardcover ISBN:

9783110182200

Pages and Images/Illustrations in book

Front matter:

8

Main content:

278

https://doi.org/10.1515/9783110199741

eBook ISBN: 9783110199741

Hardcover ISBN: 9783110182200

Keywords for this book

Finite geometries; finite groups

Audience(s) for this book

Research mathematicians, in particular geometers, and computational group theorists; academic libraries

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Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com

Finite Geometries, Groups, and Computation

Overview

About this book

Author / Editor information

Topics

Table of contents

Frontmatter

Contents

A reduction algorithm for matrix groups with an extraspecial normal subgroup

A group theoretic approach to (0, 2)-geometries

Efficient presentations for the Mathieu simple group M22 and its cover

On the uniqueness of the unipotent subgroups of some Moufang sets

Symmetric rank 3 designs with regular, elementary abelian, normal subgroups

On minimal subdegrees of finite primitive permutation groups

Computing with elation groups

Finite semifields

Constructions of quasiprimitive two-arc transitive graphs of product action type

Symplectic translation planes of even order

Structural properties of Hadamard designs

On projective planes of order less than 32

Towards effective algorithms for linear groups

Finite groups that admit Kantor families

Applications of computer algebra to finite geometry

Finite translation generalized quadrangles: old results, new results, open problems

On affine designs and GMW difference sets

Dimensional dual arcs – a survey

Backmatter

Bibliographic data