On Transposed Translation Planes

• 作者: K. Satyanarayana K. V. V. N. S. Sundari Kameswari
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: t-Spread SETS TRANSLATION PLANES Transposed TRANSLATION PLANES FLAG-TRANSITIVE TRANSLATION PLANES Collineations TRANSLATION COMPLEMENT
• 年，卷（期）: 2012,（1）
• 页码范围: 35-43
• 页数: 9页
• 分类号: O1

摘要

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.