Capable group

In mathematics, in the realm of group theory, a group is said to be capable if it occurs as the inner automorphism group of some group. These groups were first studied by Reinhold Baer, who showed that a finite abelian group is capable if and only if it is a product of cyclic groups of orders "n"1...,"n""k" where "n""i" divides "n""i"+1 and "n""k"–1="n""k".