Bases for Primitive Permutation Groups and a Conjecture of Babai

David Gluck; Ákos Seress; Aner Shalev

doi:10.1006/jabr.1997.7149

Bases for Primitive Permutation Groups and a Conjecture of Babai

David Gluck^*, Ákos Seress, Aner Shalev

^*Corresponding author for this work

Einstein Institute of Mathematics

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

18 Scopus citations

Abstract

Abaseof a permutation groupGis a sequenceBof points from the permutation domain such that only the identity ofGfixesBpointwise. We show that primitive permutation groups with no alternating composition factors of degree greater thandand no classical composition factors of rank greater thandhave a base of size bounded above by a function ofd. This confirms a conjecture of Babai.

Original language	English
Pages (from-to)	367-378
Number of pages	12
Journal	Journal of Algebra
Volume	199
Issue number	2
DOIs	https://doi.org/10.1006/jabr.1997.7149
State	Published - 15 Jan 1998

Bibliographical note

Funding Information:
* The first two authors were partially supported by NSA Grant MDA 904-95-H-1027 and NSF Grant CCR-9503430, respectively. The third author thanks the University of Chicago and All Souls College, Oxford, for their hospitality while this work was carried out.

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10.1006/jabr.1997.7149

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abstract = "Abaseof a permutation groupGis a sequenceBof points from the permutation domain such that only the identity ofGfixesBpointwise. We show that primitive permutation groups with no alternating composition factors of degree greater thandand no classical composition factors of rank greater thandhave a base of size bounded above by a function ofd. This confirms a conjecture of Babai.",

author = "David Gluck and {\'A}kos Seress and Aner Shalev",

note = "Funding Information: * The first two authors were partially supported by NSA Grant MDA 904-95-H-1027 and NSF Grant CCR-9503430, respectively. The third author thanks the University of Chicago and All Souls College, Oxford, for their hospitality while this work was carried out.",

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Bases for Primitive Permutation Groups and a Conjecture of Babai

Abstract

Bibliographical note

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