The Higman-Sims sporadic simple group as the automorphism group of resolvable $3$-designs

Rahimipour, Ali Reza

doi:10.22108/toc.2023.132404.1956

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	The Higman-Sims sporadic simple group as the automorphism group of resolvable $3$-designs
Transactions on Combinatorics
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نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2023.132404.1956
نویسنده
Ali Reza Rahimipour^*
Department of Mathematics, Faculty of Science, University of Qom, P.O. Box 37161−46611, Qom, I. R. Iran
چکیده
Presenting sporadic simple groups as an automorphism groups of designs and graphs is an exciting field in finite group theory. In this paper, with two different methods, we present some new resolvable simple $3$-designs with Higman-Sims sporadic simple group $\rm HS$ as the full automorphism group. Also, we classify all block-transitive self-orthogonal designs on 176 points with even block size that admit sporadic simple group $\rm HS$ as an automorphism group. Furthermore, with these methods we construct some new resolvable $3$-designs on 36, 40, 120 and 176 points.
کلیدواژه‌ها
$t$-design؛ resolvable design؛ sporadic simple group

مراجع
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The Higman-Sims sporadic simple group as the automorphism group of resolvable $3$-designs