Why Denote Group Operation with Multiplication?? When groups are introduced in most abstract algebra texts, the operation is denoted by multiplication or juxtaposition and addition notation is reserved for abelian groups. This seems to cause a lot of unnecessary confusion. Professors often rely completely on modular arithmetic (additive) to motivate arbitrary quotient groups (multiplicative), so students must constantly translate between the two notations. Other key examples of groups are the integers, rationals, reals and complex numbers, all under addition. When rings are introduced there is even more confusion, since the group aspect of a ring is denoted by addition, and a ring under multiplication is not a group at all. It seems to me that it would make more sense to introduce monoids with the multiplication/juxtaposition notation (to emphasize connection to rings) and use addition for group notation. One might argue that it is important to distinguish between abelian and nonabelian groups. In this case, a more acceptable notation for nonabelian groups could be the composition notation of functions. In particular this would highlight the connection to the group of bijections of a set and avoid confusion with multiplication in a ring. What do you guys think? I'm not too far into math myself, so I might have overlooked a key reason that multiplicative notation is used for groups.