Some authors use $e$ to be the identity element of a group instead of $1$. What is the origin of this notation? Was this before or after we used $e$ to represent the base of the natural logarithm? If after, is there some connection?
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We germans (or Kraut, as you might call us) call the identity element "Einheitselement", and hence denote it by $e$ (even though of course not every one does). Similarily it is common to denote a field by $k$ for "Körper"; anyway a great deal of mathematical terminology is of german origin. Likewise the french often denote vector spaces by $E$ ("espace").