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, ..., nk where ni divides ni{{hairsp}}+1 and nk{{hairsp}}−1 = nk.
References
- {{citation|first=Reinhold|last= Baer|title=Groups with preassigned central and central quotient group|journal=Transactions of the American Mathematical Society|volume=44|pages= 387–412|year=1938|issue= 3|jstor=1989887|doi=10.2307/1989887|doi-access=free}}
External links
- [https://www.ams.org/proc/2005-133-12/S0002-9939-05-07663-X/S0002-9939-05-07663-X.pdf Bounds on the index of the center in capable groups]
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