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On Doubly Transitive Groups of Degree n and Order 2(n − 1)n

Published online by Cambridge University Press:  22 January 2016

Noboru Ito
Noboru Ito*
Affiliation:
Mathematical Institute, Nagoya University
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Let 5 denote the icosahedral group and let be the normalizer of a Sylow 5-subgroup of 5. Then the index of in 5 equals six. Let us represent 5 as a permutation group A on the set of residue classes of with respect to 5 Then it is clear that A is doubly transitive of degree 6 and order 60 = 2·5·6. Since 5 is simple, A does not contain a regular normal subgroup.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 2 , July 1966 , pp. 409 - 417
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

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