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Hopf-Galois structures of isomorphic-type on a non-abelian characteristically simple extension


Author: Cindy (Sin Yi) Tsang
Journal: Proc. Amer. Math. Soc. 147 (2019), 5093-5103
MSC (2010): Primary 16W20, 20B35, 20D05; Secondary 12F10, 16T05
DOI: https://doi.org/10.1090/proc/14627
Published electronically: July 30, 2019
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Abstract: Let $ L/K$ be a finite Galois extension whose Galois group $ G$ is non-abelian and characteristically simple. By drawing tools from graph theory and group theory, we shall give a closed formula for the total number of Hopf-Galois structures on $ L/K$ with associated group isomorphic to $ G$.


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Additional Information

Cindy (Sin Yi) Tsang
Affiliation: School of Mathematics (Zhuhai), Sun Yat-Sen University, People’s Republic of China
Email: zengshy26@mail.sysu.edu.cn

DOI: https://doi.org/10.1090/proc/14627
Received by editor(s): November 29, 2018
Received by editor(s) in revised form: March 9, 2019, and March 13, 2019
Published electronically: July 30, 2019
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2019 American Mathematical Society