Geodesic
Finite groups with $2$-closed or $2'$-closed centralizers of involutions
Matematičeskie zametki, Tome 10 (1971) no. 4, pp. 437-446 
V. M. Sitnikov. Finite groups with $2$-closed or $2'$-closed centralizers of involutions. Matematičeskie zametki, Tome 10 (1971) no. 4, pp. 437-446. http://geodesic.mathdoc.fr/item/MZM_1971_10_4_a7/
@article{MZM_1971_10_4_a7,
     author = {V. M. Sitnikov},
     title = {Finite groups with $2$-closed or $2'$-closed centralizers of involutions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {437--446},
     year = {1971},
     volume = {10},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1971_10_4_a7/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Finite nonsolvable groups are described whose involution centralizers are $2$-closed or $2'$-closed, whereas the Sylow $p$-subgroups for $p>2$ are cyclic.