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博碩士論文 etd-0717108-172102 詳細資訊
Title page for etd-0717108-172102
論文名稱
Title
由交換群所定義之拉丁方陣的垂直性
Orthogonality of Latin squares defined by abelian groups
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
33
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2008-07-16
繳交日期
Date of Submission
2008-07-17
關鍵字
Keywords
垂直性、橫截、拉丁方陣
Latin square, transversal, orthogonality
統計
Statistics
本論文已被瀏覽 5704 次,被下載 2025
The thesis/dissertation has been browsed 5704 times, has been downloaded 2025 times.
中文摘要
令G為有限交換群,且LG為交換群所定義的拉丁方陣。令k(G)記作為包含LG彼此互相垂直的拉丁方陣個數之最大值。在1948年,Paige證明了若G的2-Sylow子群不是循環群,則LG就有橫截。在論文裡,我們對此定理給了建構性的証明以及討論k(G)的上界與下界。
Abstract
Let G = {g1, …,gn} be a finite abelian group, and let LG = [gij ] be the Latin square defined by gij = gi + gj. Denote by k(G) the largest number of mutually orthogonal system containing LG. In 1948, Paige
showed that if the Sylow 2-subgroup of G is not cyclic, then LG has a transversal. In this paper, we give an constructive proof for this theorem and give some upper bound and lower bound for the number k(G).
目次 Table of Contents
1.Introduction 1
2.Transveral of Latin square 3
3.Orthogonal Latin square 11
4.Appendix 19
Reference 27
參考文獻 References
[1] N. Alon, Additive Latin transversals, Israel J. Math., 117 (2000) 125-130.
[2] M. F. Atiyah; I. G. Macdonald, Introduction to commutative algebra. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. 1969
[3] S. Dasgupta, G. Karolyi, O. Serra and B. Szegedy, Transversals of additive Latin squares, Israel J. Math., 126 (2001) 17-28.
[4] I. N. Herstein, Topics in algebra. Second edition. Xerox College Publishing, Lexington, Mass.-Toronto, Ont., 1975.
[5] A. Ian, Combinatorial designs and tournaments. Oxford Lecture Series in Mathematics and its Applications, 6. The Clarendon Press, Oxford University Press, New York, 1997.
[6] L. J. Paige, Complete mappings of finite groups, Pacific J. Math., 1 (1951), 111-116.
[7] L. J. Paige, A note on finite abelian group, Bull. Amer. Math. Soc, (1948) 590-593.
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