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Glasnik matematički, Vol. 58 No. 2, 2023.

Izvorni znanstveni članak

https://doi.org/10.3336/gm.58.2.05

On symmetric \(2\)-\((70,24,8)\) designs with an automorphism of order \(6\)

Sanja Rukavina orcid id orcid.org/0000-0003-3365-7925 ; Faculty of Mathematics, University of Rijeka, 51 000 Rijeka, Croatia
Vladimir D Tonchev orcid id orcid.org/0000-0003-1806-3571 ; Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, USA

Puni tekst: engleski pdf 418 Kb

str. 225-232

preuzimanja: 42

citiraj

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Sažetak

In this paper we analyze possible actions of an automorphism of order six on a \(2\)-\((70, 24, 8)\) design, and give a complete classification for the action of the cyclic group of order six \(G= \langle \rho \rangle \cong Z_6 \cong Z_2 \times Z_3\), where \(\rho^3\) fixes exactly \(14\) points (blocks) and \(\rho^2\) fixes \(4\) points (blocks). Up to isomorphism there are \(3718\) such designs. This result significantly increases the number of
previously known \(2\)-\((70,24,8)\) designs.

Ključne riječi

Symmetric design, automorphism group

Hrčak ID:

312012

URI

https://hrcak.srce.hr/312012

Datum izdavanja:

2.5.2024.

Posjeta: 119 *

Publication date: 27 December 2023

Volume: Vol 58

Issue: Svezak 2

Pages: 225-232

DOI: 10.3336/gm.58.2.05

Article Information (continued)

Categories:

Subject: Izvorni znanstveni članak

Keywords:

Keyword: Symmetric design, automorphism group

On symmetric \(2\)-\((70,24,8)\) designs with an automorphism of order \(6\)

Sanja Rukavina[1]

Email: sanjar@math.uniri.hr

Vladimir D Tonchev[2]

Email: tonchev@mtu.edu

 

[1] Faculty of Mathematics, University of Rijeka, 51 000 Rijeka, Croatia

[2] Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, USA

Abstract

In this paper we analyze possible actions of an automorphism of order six on a \(2\)-\((70, 24, 8)\) design, and give a complete classification for the action of the cyclic group of order six \(G= \langle \rho \rangle \cong Z_6 \cong Z_2 \times Z_3\), where \(\rho^3\) fixes exactly \(14\) points (blocks) and \(\rho^2\) fixes \(4\) points (blocks). Up to isomorphism there are \(3718\) such designs. This result significantly increases the number of previously known \(2\)-\((70,24,8)\) designs.

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