Construction of the Outer Automorphism of S6 via a Complex Hadamard Matrix

Neil I. Gillespie; Padraig Ó Catháin; Cheryl E. Praeger

doi:10.1007/s11786-018-0382-0

Construction of the Outer Automorphism of S₆ via a Complex Hadamard Matrix

Neil I. Gillespie^*
, Padraig Ó Catháin
, Cheryl E. Praeger

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

1 Citation (Scopus)

308 Downloads (Pure)

Abstract

We give a new construction of the outer automorphism of the symmetric group on six points. Our construction features a complex Hadamard matrix of order six containing third roots of unity and the algebra of split quaternions over the real numbers.

Original language	English
Pages (from-to)	453-458
Number of pages	6
Journal	Mathematics in Computer Science
Volume	12
Issue number	4
Early online date	26 Sept 2018
DOIs	https://doi.org/10.1007/s11786-018-0382-0
Publication status	Published - Dec 2018

Keywords

Complex hadamard matrix
Outer automorphism
Symmetric group

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title = "Construction of the Outer Automorphism of S6 via a Complex Hadamard Matrix",

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AB - We give a new construction of the outer automorphism of the symmetric group on six points. Our construction features a complex Hadamard matrix of order six containing third roots of unity and the algebra of split quaternions over the real numbers.

KW - Complex hadamard matrix

KW - Outer automorphism

KW - Symmetric group

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