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**Automorphism group of plane curve computed by Galois points. II.**
*(English)*
Zbl 1396.14025

Summary: Recently, the first author [Proc. Japan Acad., Ser. A 94, No. 6, 59–63 (2018; Zbl 1396.14025)] classified finite groups obtained as automorphism groups of smooth plane curves of degree \(d\geq4\) into five types. He gave an upper bound of the order of the automorphism group for each types. For one of them, the type (a-ii), that is given by \(\max \{2d(d-2),60d\}\). In this article, we shall construct typical examples of smooth plane curve \(C\) by applying the method of Galois points, whose automorphism group has order \(60d\). In fact, we determine the structure of the automorphism group of those curves.

For part I, see [K. Miura and A. Ohbuchi, Beitr. Algebra Geom. 56, No. 2, 695–702 (2015; Zbl 1327.14145)].

For part I, see [K. Miura and A. Ohbuchi, Beitr. Algebra Geom. 56, No. 2, 695–702 (2015; Zbl 1327.14145)].

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\textit{T. Harui} et al., Proc. Japan Acad., Ser. A 94, No. 6, 59--63 (2018; Zbl 1396.14025)

### References:

[1] | H. F. Blichfeldt, Finite collineation groups, with an introduction to the theory of groups of operators and substitution groups, Univ. of Chicago Press, Chicago, Ill., 1917. |

[2] | S. Fukasawa, On the number of Galois points for a plane curve in positive characteristic. III, Geom. Dedicata 146 (2010), 9–20. · Zbl 1191.14035 |

[3] | T. Harui, Automorphism groups of smooth plane curves, arXiv:1306.5842v2. · Zbl 1070.14035 |

[4] | K. Miura, Field theory for function fields of singular plane quartic curves, Bull. Austral. Math. Soc. 62 (2000), no. 2, 193–204. · Zbl 0986.14016 |

[5] | K. Miura and A. Ohbuchi, Automorphism group of plane curve computed by Galois points, Beitr. Algebra Geom. 56 (2015), no. 2, 695–702. · Zbl 1327.14145 |

[6] | K. Miura and H. Yoshihara, Field theory for function fields of plane quartic curves, J. Algebra 226 (2000), no. 1, 283–294. · Zbl 0983.11067 |

[7] | H. Yoshihara, Function field theory of plane curves by dual curves, J. Algebra 239 (2001), no. 1, 340–355. · Zbl 1064.14023 |

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