Abstract
One of the fundamental problems in the theory of varieties of groups is to decide whether the laws (identical relations) of each group admit a finite basis (in the sense that they are all consequences of a finite set of laws). Oates & Powell recently proved (1964) that the answer is affirmative in the case of finite groups. We present a considerably shortened proof of their result; with a little additional reasoning, this in fact yields a slight generalization of the Oates-Powell theorem.
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