Limits for the Number of Solutions of Certain General Types of Equations in a Finite Field.

of A. Cayley. On the other -hand, W. R. Hamilton did not use the term group but favored the use of his own term quaternions for the development of a theory based upon the special abstract group of order S which-involves 6 operators of order 4. The associative law was later very commonly embodied in the definitions of an abstract group and the development of these groups did much to emphasize the fundamental importance of this law. These observations in regard to W. R. Hamilton seem to imply that the theory of abstract groups may reasonably be regarded as about ten years older than the assumption that A. Cayley was the founder of this theory would imply. Implicitly, W. R. Hamilton emphasized the importance of the quaternion group in his Lectures on Quaternions, page xxvi (1853).