| Project/Area Number |
19J14198
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| Research Category |
Grant-in-Aid for JSPS Fellows
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| Allocation Type | Single-year Grants |
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| Section | 国内 |
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| Review Section |
Basic Section 11020:Geometry-related
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| Research Institution | Ehime University |
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Principal Investigator |
YANEZ SALAZAR VICTOR H 愛媛大学, 理工学研究科, 特別研究員(DC2)
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| Project Period (FY) |
2019-04-25 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 2020: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2019: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | SSGP / MinAP / Lie group / Locally compact group / NSS group / Connected group / Bohr topology / algebraic SSGP / Divisible group / p-component / Rank of a group / Divisible rank |
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| Outline of Research at the Start |
We investigate the algebraic structure of topological groups having the following properties: minimally almost periodic, (algebraic) SSGP and extremely amenable. Our ideal goal is to establish a link between the ASSGP property and extreme amenability, contributing towards the Glasner-Pestov problem.
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| Outline of Annual Research Achievements |
A topological group has no small subgroups (NSS) if there exists an open neighborhood of the identity containing no other subgroup but the trivial one. We modelled two properties based on minimal almost periodicity (MinAP).
(A) Let C be a class of topological groups. A topological group G is said to have the MinAP(C) property if any non-trivial homomorphism from G to a group contained in C is discontinous. (B) Let P be a property of topological groups. We say that a topological group G is MinAP modulo P if and only if every continuous homomorphic image of G in a compact group has property P. If C is the class of compact groups, then MinAP(C) is the MinAP property of von Neumann. Similarly, if P is the property of being the trivial group, then MinAP modulo P coincides with MinAP
We considered the MinAP(Lie), MinAP(NSS) and MinAP(LC) properties (LC stands for locally compact). MinAP(NSS) and MinAP(LC) both imply MinAP(Lie), and MinAP(Lie) implies the MinAP property. We show that none of these implications are reversible. In Abelian topological groups, MinAP(LC), MinAP(Lie) and MinAP are equivalent, while the class of Abelian MinAP(NSS) groups coincides with the union over all ordinals α of the SSGP(α) classes of Dikranjan and Shakhmatov.
We proved that if P is preserved by continuous homomorphisms, then a group G is MinAP modulo P if and only if the quotient of G with its von Neumann kernel has property P in its Bohr topology. We described the algebraic structure of Abelian MinAP modulo P groups for the following properties P: finite, bounded, torsion, connected and compact.
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| Research Progress Status |
令和2年度が最終年度であるため、記入しない。
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| Strategy for Future Research Activity |
令和2年度が最終年度であるため、記入しない。
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