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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Characters and generosity of permutation groups

Author: Jan Saxl
Journal: Proc. Amer. Math. Soc. 47 (1975), 73-76
MathSciNet review: 0357563
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Abstract | References | Additional Information

Abstract: A necessary and sufficient character condition is obtained for a group $ G$ to be generously $ k$-fold transitive. This is similar to an old theorem of Frobenius on multiply transitive groups.

References [Enhancements On Off] (What's this?)

  • [1] Eiichi Bannai, A note on characters of normal subgroups of multiply transitive permutation groups, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 20 (1973), 373–376. MR 0335612 (49 #392)
  • [2] A. J. Coleman, Induced representations with applications to 𝑆_{𝑛} and 𝐺𝐿(𝑛), Lecture notes prepared by C. J. Bradley. Queen’s Papers in Pure and Applied Mathematics, No. 4, Queen’s University, Kingston, Ont., 1966. MR 0202859 (34 #2718)
  • [3] G. Frobenius, Über die Charactere der mehrfach transitiven Gruppen, Berliner Berłichte, 1904, 558-571.
  • [4] R. A. Liebler and M. R. Vitale, Ordering the partition characters of the symmetric group, J. Algebra 25 (1973), 487–489. MR 0316544 (47 #5091)
  • [5] H. Nagao, Multiply transitive permutation groups, Lecture Notes, California Institute of Technology, Pasadena, 1967.
  • [6] P. M. Neumann, Generosity and characters of multiply transitive permutation groups (submitted for publication).
  • [7] J. Saxl, Multiply transitive permutation groups, Ph.D. Thesis, Oxford, 1973.
  • [8] Ernst Snapper, Group characters and nonnegative integral matrices, J. Algebra 19 (1971), 520–535. MR 0284523 (44 #1748)

Additional Information

PII: S 0002-9939(1975)0357563-X
Article copyright: © Copyright 1975 American Mathematical Society

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