Abstract
Let đș be a finite permutation group on Ω.
An ordered sequence
Funding source: Australian Research Council
Award Identifier / Grant number: DE230100579
Funding statement: The first author acknowledges the support of an Australian Research Council Discovery Early Career Researcher Award (project number DE230100579).
Acknowledgements
The authors also thank the referee for their careful reading and helpful suggestions.
-
Communicated by: Timothy C. Burness
References
[1] R.âF. Bailey, Uncoverings-by-bases for base-transitive permutation groups, Des. Codes Cryptogr. 41 (2006), no. 2, 153â176. 10.1007/s10623-006-9005-xSuche in Google Scholar
[2] T.âC. Burness, On base sizes for actions of finite classical groups, J. Lond. Math. Soc. (2) 75 (2007), no. 3, 545â562. 10.1112/jlms/jdm033Suche in Google Scholar
[3] T.âC. Burness, R.âM. Guralnick and J. Saxl, On base sizes for symmetric groups, Bull. Lond. Math. Soc. 43 (2011), no. 2, 386â391. 10.1112/blms/bdq123Suche in Google Scholar
[4] T.âC. Burness, M.âW. Liebeck and A. Shalev, Base sizes for simple groups and a conjecture of Cameron, Proc. Lond. Math. Soc. (3) 98 (2009), no. 1, 116â162. 10.1112/plms/pdn024Suche in Google Scholar
[5] T.âC. Burness, E.âA. OâBrien and R.âA. Wilson, Base sizes for sporadic simple groups, Israel J. Math. 177 (2010), 307â333. 10.1007/s11856-010-0048-3Suche in Google Scholar
[6] J. CĂĄceres, D. Garijo, A. GonzĂĄlez, A. MĂĄrquez and M.âL. Puertas, The determining number of Kneser graphs, Discrete Math. Theor. Comput. Sci. 15 (2013), no. 1, 1â14. 10.46298/dmtcs.634Suche in Google Scholar
[7] P.âJ. Cameron, Permutation Groups, London Math. Soc. Stud. Texts 45, Cambridge University, Cambridge, 1999. Suche in Google Scholar
[8] P.âJ. Cameron and D.âG. Fon-Der-Flaass, Bases for permutation groups and matroids, European J. Combin. 16 (1995), no. 6, 537â544. 10.1016/0195-6698(95)90035-7Suche in Google Scholar
[9] N. Gill, B. LodĂ and P. Spiga, On the height and relational complexity of a finite permutation group, Nagoya Math. J. 246 (2022), 372â411. 10.1017/nmj.2021.6Suche in Google Scholar
[10] Z. Halasi, On the base size for the symmetric group acting on subsets, Studia Sci. Math. Hungar. 49 (2012), no. 4, 492â500. 10.1556/sscmath.49.2012.4.1222Suche in Google Scholar
[11] A. Lucchini, M. Morigi and M. Moscatiello, Primitive permutation IBIS groups, J. Combin. Theory Ser. A 184 (2021), Paper No. 105516. 10.1016/j.jcta.2021.105516Suche in Google Scholar
[12] T. Maund, Bases for permutation groups, D. Phil. thesis, Oxford University, 1989. Suche in Google Scholar
[13] J. Morris and P. Spiga, On the base size of the symmetric and the alternating group acting on partitions, J. Algebra 587 (2021), 569â593. 10.1016/j.jalgebra.2021.08.009Suche in Google Scholar
[14] M. Moscatiello and C.âM. Roney-Dougal, Base sizes of primitive permutation groups, Monatsh. Math. 198 (2022), no. 2, 411â443. 10.1007/s00605-021-01599-5Suche in Google Scholar
[15] M. Suzuki, On a class of doubly transitive groups, Ann. of Math. (2) 75 (1962), 105â145. 10.2307/1970423Suche in Google Scholar
[16] The GAP Group. GAP â Groups, Algorithms, and Programming, Version 4.9.3, 2018. Suche in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Hochschild cohomology of symmetric groups and generating functions
- StiefelâWhitney classes of representations of SL(2, đ)
- A classification of finite primitive IBIS groups with alternating socle
- On the converse of GaschĂŒtzâ complement theorem
- Conjugacy classes of maximal cyclic subgroups
- Morse boundaries of graphs of groups with finite edge groups
- The number of locally invariant orderings of a group
- On limits of betweenness relations
Artikel in diesem Heft
- Frontmatter
- Hochschild cohomology of symmetric groups and generating functions
- StiefelâWhitney classes of representations of SL(2, đ)
- A classification of finite primitive IBIS groups with alternating socle
- On the converse of GaschĂŒtzâ complement theorem
- Conjugacy classes of maximal cyclic subgroups
- Morse boundaries of graphs of groups with finite edge groups
- The number of locally invariant orderings of a group
- On limits of betweenness relations