Geodesic
Finite $2$-groups with a non-Dedekind non-metacyclic norm of Abelian non-cyclic subgroups
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2019), pp. 3-19

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The authors study finite $2$-groups with non-Dedekind non-metacyclic norm $N_{G}^{A}$ of Abelian non-cyclic subgroups depending on the cyclicness or the non-cyclicness of the center of a group $G$. The norm $N_{G}^{A}$ is defined as the intersection of the normalizers of Abelian non-cyclic subgroups of $G$. It is found out that such $2$-groups are cyclic extensions of their norms of Abelian non-cyclic subgroups. Their structure is described. 
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     author = {Fedir Lyman and Tetyana Lukashova and Marina Drushlyak},
     title = {Finite $2$-groups with a {non-Dedekind} non-metacyclic norm of {Abelian} non-cyclic subgroups},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
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Fedir Lyman; Tetyana Lukashova; Marina Drushlyak. Finite $2$-groups with a non-Dedekind non-metacyclic norm of Abelian non-cyclic subgroups. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2019), pp. 3-19. http://geodesic.mathdoc.fr/item/BASM_2019_1_a0/