Timeline for Why is the identity element of a group denoted by $e$?
Current License: CC BY-SA 3.0
6 events
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| Jul 10, 2015 at 18:13 | comment | added | Jan-Christoph Schlage-Puchta | @Tobias Fritz: No. First they define group as a group of permutations: "Hat eine Gesamtheit von Substitutionen die Eigenschaft, dass jedes Produkt von irgend zweien derselben selbst in ihr enthalten ist, so heisst sie eine Gruppe." (p. 211: Has a set of substitutions the property that every product of any two of them is again in this set, then this set is called a group). Then on p. 217, they define a general group by giving the axioms for a cancelative semigroup, and then state that if in addition the group is finite, inverses and an identity exist. | |
| Jul 10, 2015 at 17:30 | comment | added | Tobias Fritz | For German speakers: am I missing something, or does Burkhardt's Encyklopädie really define a "group" as a cancellative semigroup, and then claim that the existence of the unit and inverses follow? | |
| Apr 28, 2015 at 23:23 | comment | added | Francois Ziegler | @EmilJeřábek I agree that without further evidence of the transition, it's hard to tell how influential F & S's (pervasively used) E was in the eventual choice of e. They do tie it with eins insofar as their term for the unit is also Klasse von 1 (in quote above). | |
| Apr 28, 2015 at 11:04 | comment | added | Emil Jeřábek | I'm confused. So, the conclusion is that the choice of E by Frobenius and Stickelberger is unmotivated (as their term for the unit is Hauptelement), and its identification with Einheit by later researchers (such as Burkhardt) is a false etymology? | |
| Apr 28, 2015 at 4:26 | history | edited | Francois Ziegler | CC BY-SA 3.0 |
fixed italics
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| Apr 26, 2015 at 17:36 | history | answered | Francois Ziegler | CC BY-SA 3.0 |