Geodesic
On finite $3$-generated $2$-groups of Alperin
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 155-168 
B. M. Veretennikov. On finite $3$-generated $2$-groups of Alperin. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 155-168. http://geodesic.mathdoc.fr/item/SEMR_2007_4_a11/
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     author = {B. M. Veretennikov},
     title = {On finite $3$-generated $2$-groups of {Alperin}},
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     pages = {155--168},
     year = {2007},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2007_4_a11/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We prove a theorem about the structure of the commutant of a finite $2$-group in which every $2$-generated subgroup has a cyclic commutant and the group itself is generated by $3$ involutions. Also we construct two infinite series of such groups with the second commutant of order $2$ and $4$.

[1] Alperin J. L., “On a special class of regular groups”, Trans. Amer. Math. Soc., 106 (1963), 77–99 | MR | Zbl

[2] Veretennikov B. M., “Ob odnoi gipoteze Alperina”, Sib. matem. zhurn., 21 (1980), 200–202 | MR | Zbl

[3] Veretennikov B. M., “O konechnykh $p$-gruppakh s metatsiklicheskim kommutantom”, Sib. matem. zhurn., 39 (1998), 999–1004 | MR | Zbl