Finite Ova

[摘要] In this thesis systems consisting of a finite number of elements and one binary commutative associative rule of combination are considered. Such systems are called ova. The distinctness of ova is first discussed. The elements of ova are then classified according to their behavior when raised to powers. A necessary and sufficient condition that an ovum have no associate elements is found, and ova having no associate elements are discussed in detail. A necessary and sufficient condition that an ovum be a finite Abelian group is also found. All the distinct ova of orders 2,3,4, have been computed and are listed in the course of the paper. There are 3 distinct ova of order 2, 12 of order 3, and 56 of order 4. All concepts introduced in the discussion are illustrated in these ova.

[发布机构] University:California Institute of Technology;Department:Physics, Mathematics and Astronomy

[关键词] Mathematics