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From: gwyn@brl-smoke.UUCP
Newsgroups: net.math
Subject: Re: Groups, Alternative Definitions?
Message-ID: <1638@brl-smoke.ARPA>
Date: Sat, 8-Mar-86 18:01:28 EST
Article-I.D.: brl-smok.1638
Posted: Sat Mar  8 18:01:28 1986
Date-Received: Tue, 11-Mar-86 01:08:56 EST
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Organization: Ballistic Research Lab (BRL)
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Karl Dahlke observes that the group axioms need only specify
right- (or left-) inverses instead of two-sided inverses, since
the latter may be deduced from the former.  There are other
possible formulations of the group axioms.  For example,
uniqueness of inverse can be dropped since it follows as a
consequence of the weaker formulation anyway.  Textbook
presentations of group theory (e.g. Herstein) usually have
several exercises in which one is to show that an apparently
weaker set of axioms for a (set,operator) is sufficient to
make the (set,operator) constitute a group.

Group theory news item:  The latest BAMS contains a tutorial
article by Gorenstein on the group classification theorem.