Automorphism groups of Steiner triple systems

Doyen, Jean; Kantor, William M.

doi:10.5802/alco.240

Doyen, Jean ¹; Kantor, William M.²

¹ Université Libre de Bruxelles Bruxelles 1050 Belgium
² U. of Oregon Eugene OR 97403 and Northeastern U. Boston MA 02115

Algebraic Combinatorics, Volume 5 (2022) no. 4, pp. 593-608.

Abstract

If $G$ is a finite group then there is an integer $M_{G}$ such that $,$ for $u \geq M_{G}$ and $u \equiv 1$ or $3$ (mod 6), there is a Steiner triple system $U$ on $u$ points for which $Aut U ≅ G .$ If $V$ is a Steiner triple system then there is an integer $N_{V}$ such that $,$ for $u \geq N_{V}$ and $u \equiv 1$ or $3$ $($ mod $6),$ there is a Steiner triple system $U$ on $u$ points having $V$ as an $Aut U$ -invariant subsystem such that $Aut U ≅ Aut V$ and $Aut U$ induces $Aut V$ on $V$ .

Received: 2018-08-10
Revised: 2022-03-25
Accepted: 2022-03-26
Published online: 2022-09-08

DOI: 10.5802/alco.240

Classification: 05B07, 05B25, 51E10
Keywords: Steiner triple system, Automorphism group

Author's affiliations:

Doyen, Jean ¹; Kantor, William M. ²

¹ Université Libre de Bruxelles Bruxelles 1050 Belgium
² U. of Oregon Eugene OR 97403 and Northeastern U. Boston MA 02115

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     title = {Automorphism groups of {Steiner} triple systems},
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Doyen, Jean; Kantor, William M. Automorphism groups of Steiner triple systems. Algebraic Combinatorics, Volume 5 (2022) no. 4, pp. 593-608. doi : 10.5802/alco.240. https://alco.centre-mersenne.org/articles/10.5802/alco.240/

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