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Transitive Extensions of Certain Permutation Groups of Rank 3

Published online by Cambridge University Press:  22 January 2016

Tosiro Tsuzuku
Tosiro Tsuzuku*
Affiliation:
Nagoya University
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We denote a permutation group H on a set Γ by (H, Γ). (H, Γ) is called a permutation group of rank 3 if (H, Γ) is transitive and (Ha, Γ), a ∈ Γ, has exactly three orbits, where Ha is the stabiliger of a point a, namely, {α ∈ H \aα = a}

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 31 , January 1968 , pp. 31 - 36
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

[1] Burnside, W.S., Theory of groups of finite order, 2nd. ed. Cambridge Univ. Press, 1911.Google Scholar
[2] Carmichael, R.D., Introduction to the theory of groups of finite order, Boston, 1937.Google Scholar
[3] Huppeit, B., Zweifach transitive, auflosbare Permutations-gruppen, Math. Zeitschr. 68 (1957). 126–150.Google Scholar
[4] Ito, N., A note on transitive permutation groups of degree p, Osaka Math. J. 14 (1962), 213–218.Google Scholar
[5] Wielandt, H., Finite permutation groups, Acad. Press, 1964.Google Scholar