# ALGEBRAIC COMBINATORICS

Automorphism groups of Steiner triple systems
Algebraic Combinatorics, Volume 5 (2022) no. 4, pp. 593-608.

If $G$ is a finite group then there is an integer ${M}_{G}$ such that$,$ for $u\ge {M}_{G}$ and $u\equiv 1$ or $3$ (mod 6), there is a Steiner triple system $U$ on $u$ points for which $\mathrm{Aut}\phantom{\rule{0.5pt}{0ex}}U\phantom{\rule{0.5pt}{0ex}}\cong G.$ If $V$ is a Steiner triple system then there is an integer ${N}_{V}$ such that$,$ for $u\ge {N}_{V}$ and $u\equiv 1$ or $3$ $\left($mod $6\right),$ there is a Steiner triple system $U$ on $u$ points having $V$ as an $\mathrm{Aut}\phantom{\rule{0.5pt}{0ex}}U$-invariant subsystem such that $\mathrm{Aut}\phantom{\rule{0.5pt}{0ex}}U\cong \mathrm{Aut}V$ and $\mathrm{Aut}\phantom{\rule{0.5pt}{0ex}}U$ induces $\mathrm{Aut}\phantom{\rule{0.5pt}{0ex}}V$ on $V$.

Revised:
Accepted:
Published online:
DOI: 10.5802/alco.240
Classification: 05B07,  05B25,  51E10
Keywords: Steiner triple system, Automorphism group
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
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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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