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R. H. Bruck and R. C. Bose, “The Construction of Translation Planes from Projective Spaces,” Journal of Algebra, Vol. 1, No. 1, 1964, pp. 85-102. doi.org/10.1016/0021-8693(64)90010-9

has been cited by the following article:

• TITLE: On Transposed Translation Planes

  AUTHORS: K. Satyanarayana, K. V. V. N. S. Sundari Kameswari

  KEYWORDS: t-Spread Sets; Translation Planes; Transposed Translation Planes; Flag-Transitive Translation Planes; Collineations; Translation Complement

  JOURNAL NAME: Open Journal of Discrete Mathematics, Vol.2 No.1, January 20, 2012

  ABSTRACT: This paper is devoted to the study of a translation plane π(C) associated with a t-spread set C and its transposed t-spread set C t. In this paper, an explicit matrix form of the inverse of an isomorphism from a translation plane into another translation plane associated with t-spread sets is derived and proved that two translation planes associated with t-spread sets are isomorphic if and only if their corresponding transposed translation planes are isomorphic. Further, it is shown that the transpose of a flag-transitive plane is flag-transitive and derived a necessary and sufficient condition for a translation plane π(C) to be isomorphic to its transposed translation plane.