Let $A$ is a (possibly infinite) set.
Let $G$ is a group of functions (more precisely, bijections) on $A$ with function composition.
How to call such a group?
- a group of permutations of $A$;
- a group of bijections on $A$;
I think it's typical to say:
If we do a Google Scholar search for
This group G is commonly called "the symmetric group on A", especially if A is finite. A shorthand notation is $S_A$.