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Normal subgroups of finite multiply transitive permutation groups

Published online by Cambridge University Press:  22 January 2016

Eiichi Bannai
Eiichi Bannai*
Affiliation:
Department of Mathematics, Tokyo University
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Wagner [5] and Ito [2] proved the following theorems respectively.

THEOREM OF WAGNER. Let G be a triply transitive permutation group on a set Ω = {1,2, …, n}, and let n be odd and n > 4. If H is a normal subgroup (≠1) of G, then H is also triply transitive on Ω.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 53 , May 1974 , pp. 103 - 107
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1974

References

[1] Bannai, E.: A note on characters of normal subgroups of multiply transitive permutation groups, J. Pac. Sci. Univ. Tokyo 20 (1973) 373–376.Google Scholar
[2] Ito, N.: Normal subgroups of quadruply transitive permutation groups, Hokkaido J. Math. 1 (1972) 1–6.Google Scholar
[3] Nagao, H.: Multiply transitive groups (Lecture Note), California Institute of Technology, California (1967).Google Scholar
[4] Tsuzuku, T.: Private communication.Google Scholar
[5] Wagner, A.: Normal sugbroups of triply transitive permutation groups of odd degree, Math. Zeit. 94 (1966) 219–222.Google Scholar
[6] Wielandt, H.: Finite permutation groups, Academic Press, New York and London (1964).Google Scholar