FC-center

Symbol-free definition
The FC-center of a group is the set of elements in the group whose conjugacy class is finite in size. Since the size of the conjugacy class of a product is bounded from above by the product of the sizes of the conjugacy classes, the FC-center is a subgroup.

Fixed-point operator
A group is a fixed-point under the FC-center operator if and only if it is a FC-group.