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On the Orbit Sizes of Permutation Groups on the Power Set

✍ Scribed by Thomas Michael Keller

Publisher: World Scientific Publishing Company
Year: 2000
Tongue: English
Weight: 187 KB
Volume: 7
Category: Article
ISSN: 1005-3867
DOI: 10.1007/s10011-000-0027-z

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

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