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A Characterization of the Zassenhaus Groups

Published online by Cambridge University Press:  22 January 2016

Koichiro Harada*
Affiliation:
Nagoya University
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A doubly transitive permutation group on the set of symbols Ω is called a Zassenhaus group if satisfies the following condition: the identity is the only element leaving three distinct symbols fixed.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

[1] Brauer, R. and Suzuki, M., On finite groups of even order whose 2-Sylow group is a quaternion group, Proc. Nat. Acad. Sci., Vol. 45, (1959), pp. 17571759.CrossRefGoogle Scholar
[2] Burnside, W., Theory of groups of finite order, Cambridge Univ. Press, (1911) (Second edition).Google Scholar
[3] Feit, W., On a class of doubly transitive permutation groups, Ill. J. Math., Vol. 4, (1960), pp. 170186.Google Scholar
[4] Feit, W. and Thompson, J.G., Solvability of groups of odd order, Pac. J. of Math., Vol. 13, pp. 7751028.Google Scholar
[5] Frobenius, G., Über die Charactere der mehrfach transitiven Gruppen, S.B. Preuss. Akad. Wiss. 1904.Google Scholar
[6] Gorenstein, D. and Walter, J., On finite groups with dihedral Sylow 2-subgroups, Ill. J. Math., Vol. 6, (1962), pp. 553593.Google Scholar
[7] Ito, N., On a class of doubly transitive permutation groups, Ill. J. Math., Vol. 6, (1962), pp. 341352.Google Scholar
[8] Iwahori, N., On a property of a finite group, J. of Faculty of Sci., Univ. of Tokyo, Vol. 11, (1964), pp. 4764.Google Scholar
[9] Suzuki, M., On a class of doubly transitive groups, Ann. of Math., Vol. 75, (1962), pp. 105145.Google Scholar
[10] Suzuki, M., On a finite group with a partition. Arch. Math., Vol. 7, (1961), pp. 241254.CrossRefGoogle Scholar
[11] Suzuki, M., Finite groups with nilpotent centralizers, Trans. Amer. Math. Soc., Vol. 99, (1961), pp. 425470.CrossRefGoogle Scholar
[12] Suzuki, M., A characterization of the simple groups PSL(2, q), Jour, of Math. Soc. of Japan, Vol. 20, (1968), pp. 342349.Google Scholar
[13] Wielandt, H., Finite permutation groups, Academic Press, New York, 1964.Google Scholar
[14] Zassenhaus, H., Kennzeichnung endlicher linearer Gruppen als Permutationsgruppen, Hamb. Abh. Vol. 11, (1936), pp. 1740.Google Scholar
[15] Zassenhaus, H., Über endliche Fastkörper, Hamb. Abh., Vol. 11, (1936), pp. 187220.Google Scholar