紀要論文

紀要論文

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Osaka Journal of Mathematics. 2023, 60(3), p. 493-525

CONSTRUCTION OF ONE-FIXED-POINT ACTIONS ON SPHERES OF NONSOLVABLE GROUPS I

Morimoto, Masaharu

Osaka University and Osaka Metropolitan University, Departments of Mathematics

英語

text

2023-07

Let G be a finite group. It is known that if a homotopy sphere X has a one-fixed-point smooth G-action then the dimension of X is greater than or equal to 6. It is also known that there is an effective 2-pseudofree one-fixed-point smooth G-action on the sphere Sⁿ of dimension n if and only if n is equal to 6 and G is isomorphic to the alternating group A₅ on five letters. E. Stein proved that for the group G = SL(2, 5) × Zm such that m is prime to 30, there is a 3-pseudofree one-fixed-point smooth G-action on S⁷, where Zm is a cyclic group of order m. In this article, we determine the finite groups G possessing 3-pseudofree one-fixed-point smooth G-actions on S⁶. In addition, for an arbitrary finite group G isomorphic to A₅, A₅ × Z₂, or SL(2, 5) × Zm such that m is prime to 30, we prove that there is a 3-pseudofree one-fixed-point smooth G-action on S⁷.

10.18910/92403

92403

CONSTRUCTION OF ONE-FIXED-POINT ACTIONS ON SPHERES OF NONSOLVABLE GROUPS I

Morimoto, Masaharu

Osaka University and Osaka Metropolitan University, Departments of Mathematics

英語

2023-07

Osaka Journal of Mathematics

60

3

493

525

https://hdl.handle.net/11094/92403

10.18910/92403

https://doi.org/10.18910/92403