Abstract
A group G is core-2 if and only if |H/HG|≤2 for every H≤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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