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: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2011
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/93782 http://hdl.handle.net/10220/6800 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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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