Non-existence of Hopf-Galois structures and bijective crossed homomorphisms

作者：Tsang, Cindy^*

来源：Journal of Pure and Applied Algebra, 2019, 223(7): 2804-2821.

DOI：10.1016/j.jpaa.2018.09.016

• FIELD-EXTENSIONS

By work of C. Greither and B. Pareigis as well as N. P. Byott, the enumeration of Hopf-Galois structures on a Galois extension of fields with Galois group G may be reduced to that of regular subgroups of Hol(N) which are isomorphic to G, as N ranges over all groups of order vertical bar G vertical bar, where Hol(-) denotes the holomorph. In this paper, we shall give a description of such subgroups of Hol(N) in terms of bijective crossed homomorphisms G -> N, and then use it to study two questions related to non-existence of Hopf-Galois structures.

• 出版日期2019-7
• 单位中山大学