The normalizer problem for finite groups having normal $ 2 $-complements - Jidong Guo; Liang Zhang; Jinke Hai (Electronic Research Archive)
Assume that $ H $ is a finite group that has a normal $ 2 $-complement. Under some conditions, it is proven that the normalizer property holds for $ H $. In particular, if there is a nilpotent subgroup of index $ 2 $ in $ H $, then $ H $ has the normalizer property. The result of Li, Sehgal and Parmenter, stating that the normalizer property holds for finite groups that have an abelian subgroup of index $ 2 $ is generalized.