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# 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}.

References

Baer, Reinhold (1938), "Groups with preassigned central and central quotient group",

Transactions of the American Mathematical Society 44: 387–412, JSTOR 1989887

External links

Bounds on the index of the center in capable groups

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