## Why is the identity element of a group denoted by $e$?

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The question was asked by a student, and I did not have a ready answer. I can think of the German word Einheit'', but since in German that is not how the identity element of a group is called, I doubt that is the origin. Any ideas?

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"but since in German that is not how the identity element of a group is called" ... Sometimes it is indeed called like this. Also the identity matrix is frequently or at least not rarely called 'Einheitsmatrix'. Another thought: Sometimes the identity element in a multiplicative group is called (perhaps sloppily) Einselement (where 'eins' means 'one'). – quid Feb 7 2012 at 14:09

## 1 Answer

Heinrich Weber uses Einheit and e in his Lehrbuch der Algebra (1896).

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That is almost certainly the origin, though it should be noted that one in Russian is "edinica". – Igor Rivin Feb 7 2012 at 14:58

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@Igor: The influential early textbooks on algebra tended to be written in German, unfair though that may be to those of us who grew up with English (or Russian). Quite a bit of common terminology and notation in mathematics seems to have originated in German work during the 19th century, such as the symbols `$K,k$` for fields. – Jim Humphreys Feb 7 2012 at 20:55
Well, Weber surely popularized the term. But his friend Dedekind used "einheit" before him to mean either a unit in a field, or a unit measure in geometry, and I'll bet if you look in his work you'll find it for groups. Probably if you dig into the 19th century you can find a series of earlier and earlier, vaguer and vaguer, uses of the term for a group identity. – Colin McLarty Dec 29 at 17:35
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