1-Designs Constructed from the Groups $PSL_{2}(81)$ and $PSL_{2}(89)$

Document Type : Research Paper

Author

Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran.

Abstract

In this paper, some designs from the primitive permutation representations of the groups $PSL_2(81)$ and $PSL_2(89)$ are constructed using the Key-Moori Method 1. We determine the automorphism groups of all the obtained designs and prove that the groups $PSL_2(81)$, $PSL_2(81){}^{.}2$, $PSL_2(81)\text{:}2$, $PGL_2(81)$, $P\Sigma L_2(81)$, $P\Gamma L_2(81)$, $PSL_2(89)$ and $PSL_2(89)\text{:}2$ appear as the automorphism groups of these constructed designs.

Keywords

References

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History

• Receive Date: 05 September 2021
• Revise Date: 10 January 2022
• Accept Date: 12 January 2022
• First Publish Date: 29 January 2022