On Transposed Translation Planes

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

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DOI: 10.4236/ojdm.2012.21007                

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.

Keywords

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

Conflicts of Interest

The authors declare no conflicts of interest.

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