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_i+1 and n_k–1=n_k.

References

• Baer, Reinhold (1938), "Groups with preassigned central and central quotient group", Transactions of the American Mathematical Society, 44: 387–412, JSTOR 1989887, doi:10.2307/1989887 

External links

• Bounds on the index of the center in capable groups