Notation: Exponent of a group The exponent of a group $G$ is the least positive $n$ such that $g^n = e$ for all $g \in G$. This is obviously a sensible name for the concept.
A notational awkwardness arises however when the group $G$ is abelian and written additively. I find it grating to refer to the least positive $n$ such that $\forall g \in G$ $ng = e$ as the exponent because there is nothing going on that even looks like exponentiation.
Is there an alternate terminology that can be used in this situation? 
 A: It is called period if the group is Abelian and the notation is additive, an Abelian group of period $n$: look here (Lang's "Algebra")  . The period of an element $a$ (in the additive notation) is sometimes called the order of $a$. See, for example,  Fuchs' classic book. 
A: First, I appologise since this should rather be a comment (but I cannot yet comment).
Yet, in the process of reading this question and some of the linked material I got confused, and since I very frequently use the term exponent for abelian groups denoted additively, and know various people who do likewise, I am quite interested in this, too.


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*I looked at the linked content of Fuchs's book but I failed to locate the part that Mark Sapir is referring to. (I have no access to the book at the moment, and thus would be greatful for a precise quote of the relevant part.) 
The only thing I found online is that 'periodic' is used a synonym for 'torsion', but no mention of period of a group. 

*Also in Lang I was unable to find the mentioned usage, it seems Dylan Moreland made the same experience. Indeed, it seems period of an element is used in Lang also when the notation is multiplicative. 
Sorry, for this abuse of 'answer', but I would be grateful for clarification and did not know how to express this except via and 'answer'. 
