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On a Conjecture of J.S. Frame

Published online by Cambridge University Press:  22 January 2016

Noboru Ito
Noboru Ito*
Affiliation:
Nagoya University and University of Illinois Chicago, Illinois
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Let be a transitive group of degree n, and let be the stabilizer of a symbol in ®. Then we owe to J.S. Frame the following remarkable relations between the lengths n i of the orbits of and the degrees fi of the absolutely irreducible components of the permutation matrix representation * of :

(A) If the irreducible constituents of * are all different, then the rational number

is an integer, where k is the number of the orbits of

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 30 , August 1967, pp. 79 - 81
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Frame, J.S., The degrees of the irreducible components of simply transitive permutation groups, Duke Math. J. 3, 8–17 (1937).CrossRefGoogle Scholar
[2] Frame, J.S., The double cosets of a finite group, Bull. Amer. Math. Soc. 47, 458–467 (1941).Google Scholar
[3] Wielandt, H., Finite Permutation Groups, Academic Press (1964).Google Scholar