Non-existence of Hopf–Galois structures and bijective crossed homomorphisms
Copyright policy )Non-existence of Hopf–Galois structures and bijective crossed homomorphisms
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 $\mbox{Hol}(N)$ isomorphic to $G$ as $N$ ranges over all groups of order $|G|$, where $\mbox{Hol}(-)$ denotes the holomorph. In this paper, we shall give a description of such subgroups of $\mbox{Hol}(N)$ in terms of bijective crossed homomorphisms $G\longrightarrow N$, and then use it to study two questions related to non-existence of Hopf-Galois structures.
Accepted version
- Sun Yat-sen University China (People's Republic of)
Hopf algebras and their applications, Mathematics - Number Theory, crossed homomorphisms, Separable extensions, Galois theory, simple groups, Group Theory (math.GR), regular subgroups, Hopf-Galois structures, holomorph, FOS: Mathematics, Number Theory (math.NT), quasisimple groups, Mathematics - Group Theory, Automorphisms and endomorphisms
Hopf algebras and their applications, Mathematics - Number Theory, crossed homomorphisms, Separable extensions, Galois theory, simple groups, Group Theory (math.GR), regular subgroups, Hopf-Galois structures, holomorph, FOS: Mathematics, Number Theory (math.NT), quasisimple groups, Mathematics - Group Theory, Automorphisms and endomorphisms
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