Geodesic
On finite $3$-generated $2$-groups of Alperin
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 155-168

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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 $4$. 
@article{SEMR_2007_4_a11,
     author = {B. M. Veretennikov},
     title = {On finite $3$-generated $2$-groups of {Alperin}},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {155--168},
     publisher = {mathdoc},
     volume = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2007_4_a11/}
}
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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/