Geodesic
Finite groups in which each subgroup of the commutant is invariant
Matematičeskie zametki, Tome 12 (1972) no. 6, pp. 739-746.

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We study certain properties of finite groups in which each subgroup of the commutant is invariant. Finite nonnilpotent groups with this property are completely described. 
@article{MZM_1972_12_6_a10,
     author = {I. Ya. Subbotin},
     title = {Finite groups in which each subgroup of the commutant is invariant},
     journal = {Matemati\v{c}eskie zametki},
     pages = {739--746},
     publisher = {mathdoc},
     volume = {12},
     number = {6},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_6_a10/}
}
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I. Ya. Subbotin. Finite groups in which each subgroup of the commutant is invariant. Matematičeskie zametki, Tome 12 (1972) no. 6, pp. 739-746. http://geodesic.mathdoc.fr/item/MZM_1972_12_6_a10/