Subsets close to invariant subsets for group actions

Authors:
Leonid Brailovsky, Dmitrii V. Pasechnik and Cheryl E. Praeger

Journal:
Proc. Amer. Math. Soc. **123** (1995), 2283-2295

MSC:
Primary 20B05; Secondary 20B07

MathSciNet review:
1307498

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Abstract: Let *G* be a group acting on a set and *k* a non-negative integer. A subset (finite or infinite) is called *k*-quasi-invariant if for every . It is shown that if *A* is *k*-quasi-invariant for , 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 . Certain other bounds on , in terms of both *m* and *k*, are also obtained.

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DOI:
https://doi.org/10.1090/S0002-9939-1995-1307498-3

Article copyright:
© Copyright 1995
American Mathematical Society