Subsets close to invariant subsets for group actions

Leonid Brailovsky*, Dmitrii V. Pasechnik, Cheryl E. Praeger

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Let G be a group acting on a set Ω and k a non-negative integer. A subset (finite or infinite) is called k-quasi-invariant if. It is shown that if A is k-quasi-invariant for k > 1, then there exists an invariant subset such that. Information about G-orbit intersections with A is obtained. In particular, the number m of G-orbits which have non-empty intersection with A, but are not contained in A, is at most 2k–1. Certain other bounds on, in terms of both m and k, are also obtained.

Original languageEnglish
Pages (from-to)2283-2295
Number of pages13
JournalProceedings of the American Mathematical Society
Issue number8
StatePublished - Aug 1995
Externally publishedYes


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