Rigid Steiner triple systems obtained from projective triple systems

Grannell, M. J. and Knor, M. (2014). Rigid Steiner triple systems obtained from projective triple systems. Journal of Combinatorial Designs, 22(7) pp. 279–290.

DOI: https://doi.org/10.1002/jcd.21357

Abstract

It was shown by Babai in 1980 that almost all Steiner triple systems are rigid; that is, their only automorphism is the identity permutation. Those Steiner triple systems with the largest automorphism groups are the projective systems of orders $2^n-1$. In this paper we show that each such projective system may be transformed to a rigid Steiner triple system by at most $n$ Pasch trades whenever $n\ge 4$.

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