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 n₁, ..., n_k where n_i divides n_{iTemplate:Hairsp+1} and n_{kTemplate:Hairsp−1} = n_k.

External links

• Bounds on the index of the center in capable groups

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