PRIMITIVE GROUPS WITH NO REGULAR ORBITS ON THE SET OF SUBSETS

ÁKOS SERESS

doi:10.1112/S0024609397003536

Abstract

We determine all primitive groups which do not have a regular orbit on the power set of the permutation domain. As a corollary, we also determine all families of orbit equivalent primitive permutation groups.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Moshe, Yossi 2002. ON PERMUTATION GROUPS AND PARTITIONS. Communications in Algebra, Vol. 30, Issue. 10, p. 4889.

Casolo, Carlo and Dolfi, Silvio 2007. Prime divisors of irreducible character degrees and of conjugacy class sizes in finite groups. Journal of Group Theory, Vol. 10, Issue. 5,

Konygin, A. V. 2008. On primitive permutation groups with nontrivial global stabilizers. Proceedings of the Steklov Institute of Mathematics, Vol. 261, Issue. S1, p. 113.

Dolfi, Silvio Moretó, Alexander and Navarro, Gabriel 2009. The groups with exactly one class of size a multiple of p. Journal of Group Theory, Vol. 12, Issue. 2,

GURALNICK, ROBERT M. NAVARRO, GABRIEL and TIEP, PHAM HUU 2011. Real class sizes and real character degrees. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 150, Issue. 1, p. 47.

Seress, Ákos Wong, Tsai-Lien and Zhu, Xuding 2011. Distinguishing labeling of the actions of almost simple groups. Combinatorica, Vol. 31, Issue. 4, p. 489.

Dalla Volta, Francesca and Siemons, Johannes 2012. Orbit equivalence and permutation groups defined by unordered relations. Journal of Algebraic Combinatorics, Vol. 35, Issue. 4, p. 547.

Fawcett, Joanna B. 2013. The base size of a primitive diagonal group. Journal of Algebra, Vol. 375, Issue. , p. 302.

Lockett, D. C. and Macpherson, H. D. 2013. Orbit-equivalent infinite permutation groups. Journal of Algebraic Combinatorics, Vol. 38, Issue. 4, p. 973.

Grech, Mariusz and Kisielewicz, Andrzej 2014. Symmetry groups of boolean functions. European Journal of Combinatorics, Vol. 40, Issue. , p. 1.

Halasi, Zoltán and Podoski, Károly 2015. Every coprime linear group admits a base of size two. Transactions of the American Mathematical Society, Vol. 368, Issue. 8, p. 5857.

Herr, Katrin Rehn, Thomas and Schürmann, Achill 2015. On Lattice-Free Orbit Polytopes. Discrete & Computational Geometry, Vol. 53, Issue. 1, p. 144.

Babai, László and Cameron, Peter J. 2015. Most primitive groups are full automorphism groups of edge-transitive hypergraphs. Journal of Algebra, Vol. 421, Issue. , p. 512.

Imrich, Wilfried Smith, Simon M. Tucker, Thomas W. and Watkins, Mark E. 2015. Infinite motion and 2-distinguishability of graphs and groups. Journal of Algebraic Combinatorics, Vol. 41, Issue. 1, p. 109.

Lewis, Mark L. Navarro, Gabriel Tiep, Pham Huu and Tong-Viet, Hung P. 2015. p-parts of character degrees. Journal of the London Mathematical Society, Vol. 92, Issue. 2, p. 483.

Spiga, Pablo 2016. Finite primitive groups and edge-transitive hypergraphs. Journal of Algebraic Combinatorics, Vol. 43, Issue. 3, p. 715.

Fawcett, Joanna B. and Praeger, Cheryl E. 2016. Base sizes of imprimitive linear groups and orbits of general linear groups on spanning tuples. Archiv der Mathematik, Vol. 106, Issue. 4, p. 305.

Duyan, Hülya Halasi, Zoltán and Maróti, Attila 2018. A proof of Pyber's base size conjecture. Advances in Mathematics, Vol. 331, Issue. , p. 720.

Yang, Yong and Qian, Guohua 2018. On p-parts of character degrees and conjugacy class sizes of finite groups. Advances in Mathematics, Vol. 328, Issue. , p. 356.

Devillers, Alice Morgan, Luke and Harper, Scott 2019. The distinguishing number of quasiprimitive and semiprimitive groups. Archiv der Mathematik, Vol. 113, Issue. 2, p. 127.

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PRIMITIVE GROUPS WITH NO REGULAR ORBITS ON THE SET OF SUBSETS

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