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We study groups in which, either for any biprimary or for any nonprimary subgroup, the following condition is fulfilled: The index of the product of a subgroup and its centralizer in the normalizer of the subgroup is divisible by some prime number fixed for a group. We obtain the complete description of such groups.
We study groups satisfying the following condition: for any noninvariant subgroup A, the index of the product of A and the centralizer of A in its normalizer divides a fixed (for a given group) prime number. We give the complete description ot two-step nilpotent p-groups with the above indicated property.
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