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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Characters and generosity of permutation groups
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by Jan Saxl PDF
Proc. Amer. Math. Soc. 47 (1975), 73-76 Request permission

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
  • 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 335612
  • A. J. Coleman, Induced representations with applications to $S_{n}$ and $\textrm {GL}(n)$, Queen’s Papers in Pure and Applied Mathematics, No. 4, Queen’s University, Kingston, Ont., 1966. Lecture notes prepared by C. J. Bradley. MR 0202859
  • G. Frobenius, Über die Charactere der mehrfach transitiven Gruppen, Berliner Berłichte, 1904, 558-571.
  • R. A. Liebler and M. R. Vitale, Ordering the partition characters of the symmetric group, J. Algebra 25 (1973), 487–489. MR 316544, DOI 10.1016/0021-8693(73)90095-1
  • H. Nagao, Multiply transitive permutation groups, Lecture Notes, California Institute of Technology, Pasadena, 1967. P. M. Neumann, Generosity and characters of multiply transitive permutation groups (submitted for publication). J. Saxl, Multiply transitive permutation groups, Ph.D. Thesis, Oxford, 1973.
  • Ernst Snapper, Group characters and nonnegative integral matrices, J. Algebra 19 (1971), 520–535. MR 284523, DOI 10.1016/0021-8693(71)90085-8
Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 47 (1975), 73-76
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0357563-X
  • MathSciNet review: 0357563