Geodesic
Finite 2-groups in which the set of self-centralizing abelian normal subgroups with at least three generators is empty ($SCN_3(2)=\varnothing$)
Izvestiya. Mathematics, Tome 7 (1973) no. 2, pp. 247-280 
A. D. Ustyuzhaninov. Finite 2-groups in which the set of self-centralizing abelian normal subgroups with at least three generators is empty ($SCN_3(2)=\varnothing$). Izvestiya. Mathematics, Tome 7 (1973) no. 2, pp. 247-280. http://geodesic.mathdoc.fr/item/IM2_1973_7_2_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we study finite 2-groups in which each abelian normal subgroup is metacyclic, i.e. $SCN_3(2)=\varnothing$. The main result: a finite 2-group with $SCN_3(2)=\varnothing$ is an extension of a metacyclic group by a group isomorphic to a subgroup of the dihedral group of order 8.

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