Bases for Primitive Permutation Groups and a Conjecture of Babai

David Gluck*, Ákos Seress, Aner Shalev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-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 languageAmerican English
Pages (from-to)367-378
Number of pages12
JournalJournal of Algebra
Volume199
Issue number2
DOIs
StatePublished - 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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