Regular orbits of permutation groups on the power set

Peter J. Cameron

doi:10.1016/0012-365X(86)90218-9

Regular orbits of permutation groups on the power set

Peter J. Cameron^*

^*Corresponding author for this work

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

Abstract

If a sequence of transitive permutation groups G of degree n have orders which are not too large (log|G| = o(n^{1 2}) suffices), then the number of orbits on the power set is asymptotically 2ⁿ/|G|, and almost all of these orbits are regular. This conclusion holds in particular for primitive groups.

Original language	English
Pages (from-to)	307-309
Number of pages	3
Journal	Discrete Mathematics
Volume	62
Issue number	3
DOIs	https://doi.org/10.1016/0012-365X(86)90218-9
Publication status	Published - 1 Jan 1986

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AB - If a sequence of transitive permutation groups G of degree n have orders which are not too large (log|G| = o(n 1 2) suffices), then the number of orbits on the power set is asymptotically 2n/|G|, and almost all of these orbits are regular. This conclusion holds in particular for primitive groups.

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Regular orbits of permutation groups on the power set

Abstract

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