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大学・研究所にある論文を検索できる 「EXCLUSIONS OF SMOOTH ACTIONS ON SPHERES OF THE NON-SPLIT EXTENSION OF C₂ BY SL(2, 5)」の論文概要。リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。
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EXCLUSIONS OF SMOOTH ACTIONS ON SPHERES OF THE NON-SPLIT EXTENSION OF C₂ BY SL(2, 5)

Mizerka, Piotr 大阪大学 DOI:10.18910/89989

2023.01

概要

There are four groups G fitting into a short exact sequence 1 → SL(2, 5) → G → C₂ → 1, where SL(2, 5) is the special linear group of (2 × 2)-matrices with entries in the field of five elements. Except for the direct product of SL(2, 5) and C₂, there are two other semidirect products of these two groups and just one non-semidirect product SL(2, 5).C₂, considered in this paper. It is known that each finite nonsolvable group can act on spheres with arbitrary positive number of fixed points. Clearly, SL(2, 5).C₂ is a nonsolvable group. Moreover, it turns out that SL(2, 5).C₂ possesses a free representation and as such, can potentially act pseudofreely with nonempty fixed point set on manifolds of arbitrarily large dimension. We prove that SL(2, 5).C₂ cannot act effectively with odd number of fixed points on homology spheres of dimensions less than 14. In the special case of effective one fixed point actions on homology spheres, we are able to exclude 15, 16, and 17 from the dimension of them. Moreover, we prove that 5-pseudofree one fixed point actions of SL(2, 5).C₂ on spheres do not exist.

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