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Finite Ova


Poole, Albert Roberts (1935) Finite Ova. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/H8RN-2G38.


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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Bell, Eric Temple
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1935
Record Number:CaltechTHESIS:05052010-102644606
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5773
Deposited By: Tony Diaz
Deposited On:05 May 2010 21:28
Last Modified:03 Oct 2019 23:46

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