Abstract
Abstract Let G be a finite 2-group with the property that | H : H G | ≤ 2 ${|H:H_{G}|\leq 2}$ for all subgroups H of G. Then G has an abelian normal subgroup of index at most 4 in G. This result represents an affirmative answer to Question 18.56 from the current edition of the Kourovka Notebook.
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