On the rigidity of the Figueroa replacement in PG(2, q 3)

Abstract

Let П0 be a subplane of order q of PG(2,q 3) and let G be the copy of PGL(3,q) preserving П0. The Figueroa plane Fig(q 3) is constructed by replacing some parts of the lines of PG(2,q 3) external to П0 by suitable q-subgeometries of PG(2,q 3). Moreover, Fig(q 3) inherits G from PG(2,q 3). We show that this is the unique replacement for the external lines to П0 yielding a projective plane of order q 3 admitting G as a collineation group.

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Correspondence to Alessandro Montinaro.

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Biliotti, M., Montinaro, A. On the rigidity of the Figueroa replacement in PG(2, q 3). Combinatorica 37, 375–395 (2017). https://doi.org/10.1007/s00493-015-3337-y

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Mathematics Subject Classification (2010)

  • 51E15
  • 20B25
  • 05B25