TY - JOUR

T1 - Subsets close to invariant subsets for group actions

AU - Brailovsky, Leonid

AU - Pasechnik, Dmitrii V.

AU - Praeger, Cheryl E.

PY - 1995/8

Y1 - 1995/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0000936604&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1995-1307498-3

DO - 10.1090/S0002-9939-1995-1307498-3

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AN - SCOPUS:0000936604

SN - 0002-9939

VL - 123

SP - 2283

EP - 2295

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 8

ER -