Nilpotent and abelian Hopf-Galois structures on field extensions
Byott, NP
Date: 21 February 2013
Journal
Journal of Algebra
Publisher
Elsevier
Publisher DOI
Abstract
Let L/K be a finite Galois extension of fields with group Γ . When Γ is nilpotent, we show that the problem of enumerating all
nilpotent Hopf–Galois structures on L/K can be reduced to the corresponding problem for the Sylow subgroups of Γ . We use this to enumerate all nilpotent (resp. abelian) Hopf–Galois structures on a cyclic ...
Let L/K be a finite Galois extension of fields with group Γ . When Γ is nilpotent, we show that the problem of enumerating all
nilpotent Hopf–Galois structures on L/K can be reduced to the corresponding problem for the Sylow subgroups of Γ . We use this to enumerate all nilpotent (resp. abelian) Hopf–Galois structures on a cyclic extension of arbitrary finite degree. When Γ is abelian, we give conditions under which every abelian Hopf–Galois structure on L/K has type Γ . We also give a criterion on n such that every Hopf–Galois structure on a cyclic extension of degree n has cyclic type.
Mathematics and Statistics
Faculty of Environment, Science and Economy
Item views 0
Full item downloads 0