Base sizes of imprimitive linear groups and orbits of general linear groups on spanning tuples

Joanna Fawcett; Cheryl Praeger

doi:10.1007/s00013-016-0890-6

Base sizes of imprimitive linear groups and orbits of general linear groups on spanning tuples

Joanna Fawcett, Cheryl Praeger

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2 Citations (Scopus)

248 Downloads (Pure)

Abstract

© 2016, Springer International Publishing. For a subgroup L of the symmetric group (Formula presented.) , we determine the minimal base size of (Formula presented.) acting on (Formula presented.) as an imprimitive linear group. This is achieved by computing the number of orbits of GLd(q) on spanning m-tuples, which turns out to be the number of d-dimensional subspaces of Vm(q). We then use these results to prove that for certain families of subgroups L, the affine groups whose stabilisers are large subgroups of (Formula presented.) satisfy a conjecture of Pyber concerning bases.

Original language	English
Pages (from-to)	305-314
Number of pages	10
Journal	Archiv der Mathematik
Volume	106
Issue number	4
Early online date	2 Mar 2016
DOIs	https://doi.org/10.1007/s00013-016-0890-6
Publication status	Published - 1 Apr 2016

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10.1007/s00013-016-0890-6

Fawcett & Praeger, 2016 Base sizes of imprimitive linear groups and orbits of
The final publication is available at Springer via http://dx.doi.org/10.1007/s00013-016-0890-6
Accepted author manuscript, 297 KBLicence: Unspecified

Permutation Groups & their Interrelationship with the Symmetry of Graphs Codes & Geometric Configurations
Bamberg, J. (Investigator 01), Devillers, A. (Investigator 02) & Praeger, C. (Investigator 03)
ARC Australian Research Council
1/01/13 → 31/12/17
Project: Research

Cite this

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N2 - © 2016, Springer International Publishing. For a subgroup L of the symmetric group (Formula presented.) , we determine the minimal base size of (Formula presented.) acting on (Formula presented.) as an imprimitive linear group. This is achieved by computing the number of orbits of GLd(q) on spanning m-tuples, which turns out to be the number of d-dimensional subspaces of Vm(q). We then use these results to prove that for certain families of subgroups L, the affine groups whose stabilisers are large subgroups of (Formula presented.) satisfy a conjecture of Pyber concerning bases.

AB - © 2016, Springer International Publishing. For a subgroup L of the symmetric group (Formula presented.) , we determine the minimal base size of (Formula presented.) acting on (Formula presented.) as an imprimitive linear group. This is achieved by computing the number of orbits of GLd(q) on spanning m-tuples, which turns out to be the number of d-dimensional subspaces of Vm(q). We then use these results to prove that for certain families of subgroups L, the affine groups whose stabilisers are large subgroups of (Formula presented.) satisfy a conjecture of Pyber concerning bases.

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Base sizes of imprimitive linear groups and orbits of general linear groups on spanning tuples

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Permutation Groups & their Interrelationship with the Symmetry of Graphs Codes & Geometric Configurations

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