Definition of improper groups by means of axioms : a dissertation
Institution: | University of Missouri – Columbia |
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Department: | |
Year: | 1906 |
Record ID: | 1490321 |
Full text PDF: | http://hdl.handle.net/10355/15331 |
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.