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)

265 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

Access to Document

10.1007/s11786-018-0382-0Licence: CC BY

Full-text PDF (final published version)
This is the final published version of the article (version of record). It first appeared online via Springer at https://link.springer.com/article/10.1007%2Fs11786-018-0382-0 . Please refer to any applicable terms of use of the publisher.
Final published version, 399 KBLicence: CC BY

Handle.net

Persistent link

Cite this

@article{2f671c8b590344428de212aa0437a8f4,

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

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.",

keywords = "Complex hadamard matrix, Outer automorphism, Symmetric group",

author = "Gillespie, \{Neil I.\} and \{{\'O} Cath{\'a}in\}, Padraig and Praeger, \{Cheryl E.\}",

year = "2018",

month = dec,

doi = "10.1007/s11786-018-0382-0",

language = "English",

volume = "12",

pages = "453--458",

journal = "Mathematics in Computer Science",

issn = "1661-8270",

publisher = "Birkhauser Verlag Basel",

number = "4",

}

TY - JOUR

T1 - Construction of the Outer Automorphism of S6 via a Complex Hadamard Matrix

AU - Gillespie, Neil I.

AU - Ó Catháin, Padraig

AU - Praeger, Cheryl E.

PY - 2018/12

Y1 - 2018/12

N2 - 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.

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

UR - https://www.scopus.com/pages/publications/85054037444

U2 - 10.1007/s11786-018-0382-0

DO - 10.1007/s11786-018-0382-0

M3 - Article (Academic Journal)

AN - SCOPUS:85054037444

SN - 1661-8270

VL - 12

SP - 453

EP - 458

JO - Mathematics in Computer Science

JF - Mathematics in Computer Science

IS - 4

ER -