A design and a geometry for the group Fi 22

P. J. Cameron; A. Rudvalis

doi:10.1007/s10623-007-9041-1

A design and a geometry for the group Fi ₂₂

P. J. Cameron^*
, A. Rudvalis

^*Corresponding author for this work

Centre for Interdisciplinary Research in Computational Algebra

Research output: Contribution to journal › Article › peer-review

Abstract

The Fischer group Fi ₂₂ acts as a rank 3 group of automorphisms of a symmetric 2-(14080,1444,148) design. This design does not have a doubly transitive automorphism group, since there is a partial linear space with lines of size 4 defined combinatorially from the design and preserved by its automorphism group. We investigate this geometry and determine the structure of various subspaces of it.

Original language	English
Pages (from-to)	11-14
Number of pages	4
Journal	Designs, Codes, and Cryptography
Volume	44
Issue number	1-3
DOIs	https://doi.org/10.1007/s10623-007-9041-1
Publication status	Published - 1 Sept 2007

Keywords

Automorphism group
Geometry
Symmetric design

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Cite this

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title = "A design and a geometry for the group Fi 22",

abstract = "The Fischer group Fi 22 acts as a rank 3 group of automorphisms of a symmetric 2-(14080,1444,148) design. This design does not have a doubly transitive automorphism group, since there is a partial linear space with lines of size 4 defined combinatorially from the design and preserved by its automorphism group. We investigate this geometry and determine the structure of various subspaces of it.",

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AB - The Fischer group Fi 22 acts as a rank 3 group of automorphisms of a symmetric 2-(14080,1444,148) design. This design does not have a doubly transitive automorphism group, since there is a partial linear space with lines of size 4 defined combinatorially from the design and preserved by its automorphism group. We investigate this geometry and determine the structure of various subspaces of it.

KW - Automorphism group

KW - Geometry

KW - Symmetric design

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