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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 ni 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

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