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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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 |
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DRNTU::Science::Mathematics::Applied mathematics Brailovsky, Leonid. Pasechnik, Dmitrii V. Praeger, Cheryl E. Subsets close to invariant subsets for group actions |
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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. |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Brailovsky, Leonid. Pasechnik, Dmitrii V. Praeger, Cheryl E. |
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Article |
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Brailovsky, Leonid. Pasechnik, Dmitrii V. Praeger, Cheryl E. |
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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 |
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2011 |
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https://hdl.handle.net/10356/93782 http://hdl.handle.net/10220/6800 |
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