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Trace forms and self-dual normal bas...

Kang, Dong Seung.

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Trace forms and self-dual normal bases in Galois field extensions.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Trace forms and self-dual normal bases in Galois field extensions./
Author:	Kang, Dong Seung.
Description:	46 p.
Notes:	Source: Dissertation Abstracts International, Volume: 63-08, Section: B, page: 3747.
Contained By:	Dissertation Abstracts International63-08B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3061899
ISBN:	049377730X

Trace forms and self-dual normal bases in Galois field extensions.
Kang, Dong Seung.

Trace forms and self-dual normal bases in Galois field extensions. - 46 p.

Source: Dissertation Abstracts International, Volume: 63-08, Section: B, page: 3747.

Thesis (Ph.D.)--Oregon State University, 2003.

Let G be a finite group, G 2 be a Sylow 2-subgroup of G, and L/K be a G-Galois extension. We study the trace form qL/K of L/K and the question of existence of a self-dual normal basis. Our main results are as follows: (1) If G2 is not abelian and K contains certain roots of unity then qL/K is hyperbolic over K. (2) If G has a subgroup of index 2 then L/K has no orthogonal normal basis for any G-Galois extension L/K. (3) If G has even order and G2 is abelian then L/K does not have an orthogonal normal basis, for some G-Galois extension L/K.

ISBN: 049377730XSubjects--Topical Terms:

515831
Mathematics.

Trace forms and self-dual normal bases in Galois field extensions.
LDR:01637nmm 2200277 4500 001 1861823
005 20041215074110.5
008 130614s2003 eng d
020 $a 049377730X
035 $a (UnM)AAI3061899
035 $a AAI3061899
040 $a UnM $c UnM
100 1 $a Kang, Dong Seung. $3 1949403
245 1 0 $a Trace forms and self-dual normal bases in Galois field extensions.
300 $a 46 p.
500 $a Source: Dissertation Abstracts International, Volume: 63-08, Section: B, page: 3747.
500 $a Adviser: Zinovy Reichstein.
502 $a Thesis (Ph.D.)--Oregon State University, 2003.
520 $a Let G be a finite group, G 2 be a Sylow 2-subgroup of G, and L/K be a G-Galois extension. We study the trace form qL/K of L/K and the question of existence of a self-dual normal basis. Our main results are as follows: (1) If G2 is not abelian and K contains certain roots of unity then qL/K is hyperbolic over K. (2) If G has a subgroup of index 2 then L/K has no orthogonal normal basis for any G-Galois extension L/K. (3) If G has even order and G2 is abelian then L/K does not have an orthogonal normal basis, for some G-Galois extension L/K.
520 $a We also give an explicit construction of a self-dual normal basis for an odd degree abelian extension L/K, provided K contains certain roots of unity, and study the generalized trace form for an abelian group G.
590 $a School code: 0172.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 0 $a Oregon State University. $3 625720
773 0 $t Dissertation Abstracts International $g 63-08B.
790 1 0 $a Reichstein, Zinovy, $e advisor
790 $a 0172
791 $a Ph.D.
792 $a 2003
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3061899