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.