Date of Publication
4-15-1994
Document Type
Master's Thesis
Degree Name
Master of Science in Mathematics
Subject Categories
Mathematics
College
College of Science
Department/Unit
Mathematics and Statistics
Thesis Adviser
Blessilda Raposa
Defense Panel Chair
Severino V. Gervacio
Defense Panel Member
Yolando Beronque
Arlene Pascasio
Abstract/Summary
This theses presents two main theorems to determine the existence of even tournaments whose automorphism groups contain regular subgroups. A tournament with v vertices such that v = 2k + 1 is considered. The first of the two main theorems deals on the case when k = 1 (mod 4). The other one deals on the case when k = 0 (mod) 4.All the lemmas and the theorems stated by Noboru 'Ito in Note on even tournaments whose automorphism groups contain regular subgroups are provided by the thesis-writer with proofs. Other theorems necessary to the study but are not stated in Ito's note are also presented.In addition to the presentation of the theorems to determine the existence of even tournaments whose automorphism groups contain regular subgroups, a way of determining the structure of said tournaments is also presented.This thesis presents two main theorems to determine the existence of even tournaments whose automorphism groups contain regular subgroups. A tournament with v vertices such that v = 2k + 1 is considered. The first of the two main theorems deals with the case k = 1 mod 4. The other one deals with the case when k = 0 mod 4.All the lemmas and the theorems stated by Noburu Ito in Note on even tournaments whose automorphism groups contain regular subgroups are provided with proofs in this paper. Other theorems necessary in the study but are not stated in Ito's note are also presented.In addition to the presentation of the theorems to determine the existence of even tournaments whose automorphism groups contain regular subgroups, a way of determining the structure of said tournaments is also presented.
Abstract Format
html
Language
English
Format
Accession Number
TG02234
Shelf Location
Archives, The Learning Commons, 12F Henry Sy Sr. Hall
Physical Description
95 leaves
Keywords
Mathematics--Formulae; Automorphisms; Groups, Theory of; Graph theory
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Recommended Citation
Torres, E. C. (1994). On even tournaments whose automorphism groups contain regular subgroups. Retrieved from https://animorepository.dlsu.edu.ph/etd_masteral/1548
