Huczynska, Sophie (2002) Primitive free elements of Galois fields. PhD thesis, University of Glasgow.
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Abstract
The key result linking the additive and multiplicative structure of a finite field is the Primitive Normal Basis Theorem; this was established by Lenstra and Schoof in 1987 in a proof which was heavily computational in nature. In this thesis, a new, theoretical proof of the theorem is given, and new estimates (in some cases, exact values) are given for the number of primitive free elements.
A natural extension of the Primitive Normal Basis Theorem is to impose additional conditions on the primitive free elements; in particular, we may wish to specify the norm and trace of a primitive free element. The existence of at least one primitive free element of GF(qn) with specified norm and trace was established for n ³ 5 by Cohen in 2000; in this thesis, the result is proved for the most delicate cases, n = 4 and n = 3, thereby completing the general existence theorem.
Item Type:  Thesis (PhD) 

Qualification Level:  Doctoral 
Subjects:  Q Science > QA Mathematics 
Colleges/Schools:  College of Science and Engineering > School of Mathematics and Statistics > Mathematics 
Supervisor's Name:  Cohen, Prof. S.D. and Odoni, R.W.K. 
Date of Award:  2002 
Depositing User:  Mrs Marie Cairney 
Unique ID:  glathesis:20025533 
Copyright:  Copyright of this thesis is held by the author. 
Date Deposited:  24 Sep 2014 08:54 
Last Modified:  24 Sep 2014 15:05 
URI:  http://theses.gla.ac.uk/id/eprint/5533 
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