Capable group

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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,...,nk where ni divides ni+1 and nk–1=nk.


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

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