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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W.

Managing Editor: Wilson, John S. / Khukhro, Evgenii I. / Kramer, Linus

6 Issues per year

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Volume 11, Issue 6


On the single-orbit conjecture for uncoverings-by-bases

Robert F. Bailey
  • Robert F. Bailey, School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada. E-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Peter J. Cameron
  • Peter J. Cameron, School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, United Kingdom. E-mail:
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2008-09-30 | DOI: https://doi.org/10.1515/jgt.2008.053


Let G be a permutation group acting on a finite set Ω. An uncovering-by-bases (or UBB) for G is a set of bases for G such that any r-subset of Ω is disjoint from at least one base in , where , for d the minimum degree of G. The single-orbit conjecture asserts that for any finite permutation group G, there exists a UBB for G contained in a single orbit of G on its irredundant bases. We prove a case of this conjecture, for when G is k-transitive and has a base of size k + 1. Furthermore, in the more restricted case when G is primitive and has a base of size 2, we show how to construct a UBB of minimum possible size.

About the article

Received: 2007-07-18

Revised: 2007-12-03

Published Online: 2008-09-30

Citation Information: Journal of Group Theory, Volume 11, Issue 6, Pages 845–850, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: https://doi.org/10.1515/jgt.2008.053.

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