 

Nigel P. Byott
Solubility criteria for HopfGalois structures view print


Published: 
September 15, 2015 
Keywords: 
HopfGalois structure; soluble group; simple group 
Subject: 
12F10, 16T05, 20D05 


Abstract
Let L/K be a finite Galois extension of fields with group Γ.
Associated to each HopfGalois structure on L/K is a group G of
the same order as the Galois group Γ. The type of the
HopfGalois structure is by definition the isomorphism type of G.
We investigate the extent to which general properties of either of the
groups Γ and G constrain those of the other. Specifically, we
show that if G is nilpotent then Γ is soluble, and that if
Γ is abelian then G is soluble. In contrast to these results,
we give some examples where the groups Γ and G have different
composition factors. In particular, we show that a soluble extension
may admit a HopfGalois structure of insoluble type.


Author information
Department of Mathematics, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QF, UK
N.P.Byott@ex.ac.uk

