Permutation groups without exponentially many orbits on the power set

✍ Scribed by László Babai; László Pyber

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 390 KB
Volume: 66
Category: Article
ISSN: 0097-3165
DOI: 10.1016/0097-3165(94)90056-6

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Regular orbits of permutation groups on

Regular orbits of permutation groups on the power set

✍ Peter J Cameron 📂 Article 📅 1986 🏛 Elsevier Science 🌐 English ⚖ 139 KB

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.