Abstract
The subject of this article are a priori constructions of primitive elements in field extensions. Consider the totality of all separable polynomialsf of degreen over a fieldK with rootsx 1,...,x n and prescribed Galois groupG. A vector (b 1,...,b n )∈K n is called stably primitive (forG), if, for each suchf,b 1 x 1+...+b n x n generates the splitting field off. We develop representation theoretical devices to investigate the set of stably primitive vectors geometrically. A fundamental observation is that is either very large or very small (or even empty). These two cases are illustrated by various examples. Moreover, criteria are given to decide which case holds. For a number of groups where is recognized to be small we show .
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
