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From: mward@uoregon.UUCP (mward)
Newsgroups: net.math
Subject: Re: Groups, Alternative Definitions?
Message-ID: <139800006@uoregon.UUCP>
Date: Mon, 10-Mar-86 13:43:00 EST
Article-I.D.: uoregon.139800006
Posted: Mon Mar 10 13:43:00 1986
Date-Received: Fri, 14-Mar-86 07:35:44 EST
References: <370@ihnet.UUCP>
Organization: Univ of Oregon - Eugene, OR
Lines: 12
Nf-ID: #R:ihnet:-37000:uoregon:139800006:000:534
Nf-From: uoregon!mward    Mar 10 10:43:00 1986


    In my earlier response to Karl Dahlke's alternative
formulations of the group axioms I carelessly overlooked
the word "unique" in his definitions.  The example I 
mentioned shows that without the assumption of the uniqueness
of the left identity, the existence of a left identity and right
inverses does not always yield a group.  In the presence of
the uniqueness assumption on the left identity, a group is
obtained.

           Michael Ward   UUCP  . . .!tektronix!uoregon!mward
                          CSNET  mward@uoregon