Subsets close to invariant subsets for group actions

Let G be a group acting on a set Ω and k a non-negative integer. A subset (finite or infinite) A ⊆ Ω is called k-quasi-invariant if |Ag \ A| ≤k for every g ∈ G. It is shown that if A is k-quasi-invariant for k ≥1 , then there exists an invariant subset Γ⊆Ω such that |A Δ Γ | < 2ek [(In 2k)]. Info...

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Main Authors: Brailovsky, Leonid., Pasechnik, Dmitrii V., Praeger, Cheryl E.
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2011
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Online Access:https://hdl.handle.net/10356/93782
http://hdl.handle.net/10220/6800
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-937822023-02-28T19:22:29Z Subsets close to invariant subsets for group actions Brailovsky, Leonid. Pasechnik, Dmitrii V. Praeger, Cheryl E. School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Applied mathematics Let G be a group acting on a set Ω and k a non-negative integer. A subset (finite or infinite) A ⊆ Ω is called k-quasi-invariant if |Ag \ A| ≤k for every g ∈ G. It is shown that if A is k-quasi-invariant for k ≥1 , then there exists an invariant subset Γ⊆Ω such that |A Δ Γ | < 2ek [(In 2k)]. 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 |A Δ Γ |, in terms of both m and k , are also obtained. Published version 2011-05-25T04:24:40Z 2019-12-06T18:45:30Z 2011-05-25T04:24:40Z 2019-12-06T18:45:30Z 1995 1995 Journal Article Brailovsky, L., Pasechnik, D. V., & Praeger, C. E. (1995). Subsets close to invariant subsets for group actions. Proceedings of the American Mathematical Society, 123(8), 2283-2295. https://hdl.handle.net/10356/93782 http://hdl.handle.net/10220/6800 10.1090/S0002-9939-1995-1307498-3 en Proceedings of the American Mathematical Society © 1995 American Mathematical Society. This paper was published in Proceedings of the American Mathematical Society and is made available as an electronic reprint (preprint) with permission of American Mathematical Society. The paper can be found at :[DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1307498-3].One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. application/pdf
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic DRNTU::Science::Mathematics::Applied mathematics
spellingShingle DRNTU::Science::Mathematics::Applied mathematics
Brailovsky, Leonid.
Pasechnik, Dmitrii V.
Praeger, Cheryl E.
Subsets close to invariant subsets for group actions
description Let G be a group acting on a set Ω and k a non-negative integer. A subset (finite or infinite) A ⊆ Ω is called k-quasi-invariant if |Ag \ A| ≤k for every g ∈ G. It is shown that if A is k-quasi-invariant for k ≥1 , then there exists an invariant subset Γ⊆Ω such that |A Δ Γ | < 2ek [(In 2k)]. 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 |A Δ Γ |, in terms of both m and k , are also obtained.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Brailovsky, Leonid.
Pasechnik, Dmitrii V.
Praeger, Cheryl E.
format Article
author Brailovsky, Leonid.
Pasechnik, Dmitrii V.
Praeger, Cheryl E.
author_sort Brailovsky, Leonid.
title Subsets close to invariant subsets for group actions
title_short Subsets close to invariant subsets for group actions
title_full Subsets close to invariant subsets for group actions
title_fullStr Subsets close to invariant subsets for group actions
title_full_unstemmed Subsets close to invariant subsets for group actions
title_sort subsets close to invariant subsets for group actions
publishDate 2011
url https://hdl.handle.net/10356/93782
http://hdl.handle.net/10220/6800
_version_ 1759855247680864256