Definition of improper groups by means of axioms : a dissertation
Hurwitz, Wallie Abraham, 1886-1958
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Essentially, a group is an associative field, in which the inverse combinations are uniquely possible. This is a concise statement of the classical definition of a group. The conditions which it connotes will be used here as a convenient starting point for comparing various definitions of a group. It should be said, at the outset, that the accurate definition of a group will be somewhat different question according as a finite or an infinite, or an unspecified number of objects is to be dealt with. Conditions which are sufficient in one case may be found insufficient in the others.
Theses and Dissertations (MU)