Abstract
This paper considers finite groups G whose Sylow normalizers are supplemented by groups D having a cyclic Hall 2 ′ 2’ -subgroup. G is solvable and all odd order composition factors of G are cyclic. If S ∈ Syl 2 ( D ) S \in {\text {Syl}_2}(D) is cyclic, dihedral, semidihedral, or generalized quaternion, then G is almost super-solvable.
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