Orthogonality of linear (alinear) quasigroups and their parastrophes
V.A. Shcherbacov
TL;DR
This paper investigates the conditions under which various types of linear and alinear quasigroups are orthogonal, providing criteria for their parastrophe orthogonality and showing specific non-orthogonality results over symmetric groups.
Contribution
It establishes necessary and sufficient conditions for orthogonality of linear and alinear quasigroups and their parastrophes, advancing understanding of their algebraic structure.
Findings
Conditions for quasigroup orthogonality are derived.
Linear quasigroups over S_n are not orthogonal to their (12)-parastrophe for n≠2,6.
Parastrophe orthogonality criteria are provided.
Abstract
Necessary and sufficient conditions of orthogonality of left (right) linear (alinear) quasigroups in various combinations are given. As corollary we obtain conditions of parastroph orthogonality of left (right) linear (alinear) quasigroups. Any linear (alinear) quasigroup over the symmetric group S_n () is not orthogonal to its (12)-parastrophe.
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Taxonomy
TopicsMathematics and Applications · graph theory and CDMA systems · Advanced Mathematical Theories