On even tournaments whose automorphism groups contain regular subgroups

• Main Author: Torres, Ernesto C., Jr.
• Format: text
• Language: English
• Published: Animo Repository 1994
• Subjects: Mathematics > Formulae; Automorphisms; Groups, Theory of; Graph theory; Mathematics
• Online Access: https://animorepository.dlsu.edu.ph/etd_masteral/1548; https://animorepository.dlsu.edu.ph/context/etd_masteral/article/8386/viewcontent/TG02234_F_Redacted.pdf
• Institution: De La Salle University

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.