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On Permutation Groups of Prime Degree p Which Contain at Least Two Classes of Conjugate Subgroups of Index p. II1)

Published online by Cambridge University Press:  22 January 2016

Noboru Ito
Noboru Ito*
Affiliation:
Department of Mathematics, University of Illinois at Chicago Circle, Chicago, Illinois, 60680, USA
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Let p be a prime and let Ω be the set of p symbols 1,2, ..., p, called points. Let be a transitive permutation group on Ω such that

(I) contains a subgroup of index p which is not the stabilizer of a point.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 37 , March 1970 , pp. 201 - 208
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1970

Footnotes

2)

This research was partially supported by NSF Grant GP-6539.

1)

This paper is a continuation of ([7]) with the same title.

References

[1] Brauer, R., On permutation groups of prime degree and related classes of groups, Ann. of Math. (2) 44 (1943), 57–79.Google Scholar
[2] Dembowski, P., Finite geometries, Berlin Heiderberg New York 1968.CrossRefGoogle Scholar
[3] Ito, N., Über die Gruppen PSLn(q), die eine Untergruppe von Primzahlindex enthaiten. Acta Sci. Math. Szeged 21, (1960), 206–217.Google Scholar
[4] Ito, N., On a class of doubly transitive permutation groups, Illinois J. Math. 6 (1962), 341–352.Google Scholar
[5] Ito, N. Transitive permutation groups of degree p = 2q+l, p and q being prime numbers. II, Trans. Amer. Math. Soc. 113 (1964), 454–487.Google Scholar
[6] Ito, N., On a class of doubly, but not triply transitive permutation groups, Arch. Math. 18 (1967), 564–570.CrossRefGoogle Scholar
[7] Ito, N., On permutation groups of prime degree p which contain (at least) two classes of conjugate subgroups of index p , Rendiconti Sem. Mat. Padova 38 (1967), 287–292.Google Scholar
[8] Wielandt, H., Finite permutation groups, New York (1964).Google Scholar