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

Document Type : Research Paper

Author

Department of Mathematics, Faculty of Science, University of Qom, P.O. Box 37161−46611, Qom, I. R. Iran

Abstract

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.

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  • Receive Date: 19 January 2022
  • Revise Date: 02 April 2023
  • Accept Date: 11 April 2023
  • Published Online: 01 June 2024