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Capable group

Summary

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.

References edit

  • 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, JSTOR 1989887

External links edit

  • Bounds on the index of the center in capable groups