On Some Autotopisms Of Non-Steiner Central Loops

Details On Some Autotopisms Of Non-Steiner Central Loops On Some Autotopisms Of Non-Steiner Central Loops

2007-07-10

arxiv.org/abs/0707.1438v2

Journal Of Nigerian Mathematical Society, Vol. 27(2008), 53-68

Mathematics

General Mathematics

12 pages, submitted

Scientific paper

An algebraic process for the construction of an autotopism for a non-Steiner C-loop is described and this is demonstrated with an example using a known finite C-loop. In every C-loop, two of its parastrophes are not equivalent(equal) it, if and only if both the first and second components of the constructed autotopism and its inverse autotopism are not equal to the identity map. Hence, none of the other three parastrophes is equivalent(equal) to the C-loop. It is proved that the set of autotopisms that prevent a C-loop from being a Steiner loop forms a Steiner triple system.

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