In documents relating to group theory it seems common to use a multiplicative notation to represent the group operation. For example, I'm reading Herstein's "Topics in Algebra" and looking for some pointers about vector spaces in the section on groups. In the vector space section the group operation combining vectors is (quite logically) represented as addition ($v = v_1 + v_2$), but when I switch across to the section on groups it's multiplication ($c = ab$).
Besides finding the switch of notation unhelpful, I feel that the additive notation is a better analogy with real arithmetic: all group elements have an inverse as they do with addition, whereas the multiplicative notation carries an untrue suggestion that there may be a "0" which has no inverse.
So, have I missed something: is there some reason why the multiplicative notation is preferable ?