Some symmetric designs invariant under the small Ree groups

Abstract

A construction of primitive 1-designs invariant under the action of a finite primitive group is used to determine the parameters of certain symmetric 1-designs. Using a method referred to as Key–Moori Method 1, in this article we construct a number of symmetric 1-designs from the maximal subgroups of the small Ree groups ${}^2{G}_2(q)$.

Keywords:

• Small Ree groups
• designs
• conjugacy class
• maximal subgroup
• primitive permutation representation

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 20D05
• 05E15
• 05E20

Acknowledgments

The authors would like to thank the referees for their diligent reading and comments improved the content of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

J. Moori acknowledges support of NRF and NWU (Mafikeng). Bernardo G. Rodrigues acknowledges support of NRF through Grant Numbers 95725 and 106071. A. Saeidi acknowledges support of NWU (Mafikeng) postdoctoral fellowship. S. Zandi acknowledges support of NRF postdoctoral fellowship through Grant Number 91495.