# Capable group

From HandWiki

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**(3): 387–412, doi:10.2307/1989887

## External links

Original source: https://en.wikipedia.org/wiki/Capable group.
Read more |