Let G be a finite group. A subgroup H of G is called an H-subgroup of G if N_G(H) ∩ H~9 ≤ H for all g ? G; G is said to be an H_p-group if every cyclic subgroup of G of prime order or order 4 is an H-subgroup of G. In this paper, the structure of the finite groups all of whose maximal subgroups of even order are H_p-subgroups have been characterized.
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