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Keywords:

  • automorphism;
  • Pasch configuration;
  • projective triple system;
  • rigid system;
  • Steiner triple system;
  • trade;
  • AMS classifications: Primary: 05B07;
  • Secondary: 05B25, 05E18

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 inline image. 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 inline image.