Publication date: 27 December 2023
Volume: Vol 58
Issue: Svezak 2
Pages: 225-232
DOI: 10.3336/gm.58.2.05
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.org/0000-0003-3365-7925
; Faculty of Mathematics, University of Rijeka, 51 000 Rijeka, Croatia
Vladimir D Tonchev
orcid.org/0000-0003-1806-3571
; Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, USA
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.
Symmetric design, automorphism group
312012
17.8.2024.
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