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

1 July 1966

journal article
research article
Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal

Vol. 27 (2) , 409-417
https://doi.org/10.1017/s002776300002626x

Abstract

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.

Keywords

SYLOW
RESPECT
ICOSAHEDRAL
PERMUTATION
DOUBLY TRANSITIVE GROUPS
GROUPS OF DEGREE

This publication has 2 references indexed in Scilit:

Transitive extensions of dihedral groups
Mathematische Zeitschrift, 1954
On the Representation of Groups of Finite Order
Proceedings of the National Academy of Sciences, 1939