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G. Cutolo, H. Smith and J. Wiegold
On core-2 groups
J. Algebra, 237, (2001), pp. 813–841.
doi: 10.1006/jabr.2000.8599
MathSciNet Zentralblatt Comments Abstract Full Text
Abstract
A group $G$ is core-2 if and only if $|H/H_G|\le 2$ for every $H\le G$. We prove that every core-2 nilpotent 2-group of class 2 has an abelian subgroup of index at most 4. This bound is the best possible. As a consequence, every 2-group satisfying the property core-2 has an abelian subgroup of index at most 16.
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