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September 2022 Galois realization of Schur covers of dihedral groups of $2$-power order
Ryosuke Amano, Akira Ishimaru, Masanari Kida
Funct. Approx. Comment. Math. 67(1): 47-67 (September 2022). DOI: 10.7169/facm/1975

Abstract

The Schur covers of a dihedral group of $2$-power order are a dihedral group,a semi-dihedral group, and a generalized quaternion group.We prove that if one of the three groups is realizable as Galois group, thenother two groups are also realizable as Galois groups under a~condition on the existence of a certain quartic cyclic extension over the base field.

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Ryosuke Amano. Akira Ishimaru. Masanari Kida. "Galois realization of Schur covers of dihedral groups of $2$-power order." Funct. Approx. Comment. Math. 67 (1) 47 - 67, September 2022. https://doi.org/10.7169/facm/1975

Information

Published: September 2022
First available in Project Euclid: 13 April 2022

Digital Object Identifier: 10.7169/facm/1975

Subjects:
Primary: 11R32 , 12F12

Keywords: dihedral group , generalized quaternion group , inverse Galois problem , isoclinism , semi-dihedral group

Rights: Copyright © 2022 Adam Mickiewicz University

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Vol.67 • No. 1 • September 2022
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