Is there a name for operators that turns $\times$ to $+$ and $/$ to $-$?

Question

Just out of curiosity, is there an official names for functions/operator that turns $\times$ to $+$ and $/$ to $-$?

A few of examples comes to mind

• log
• exp
• argument of a complex number "arg"

Answer 1

One name for such functions would be “isomorphisms from the multiplicative group of $\ldots$ to the additive group of $\ldots$”, where the ellipses stand for whatever objects you're considering – real numbers, complex numbers, matrices, etc. An isomorphism is a bijection that respects the structure of a set, in this case the group structure. In this context, it would be more natural to talk about preserving inverses rather than mapping division to subtraction; division and subtraction can be described as multiplication by and addition of inverses, respectively.