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IMI/Publicaţii/BASM/Ediţii/BASM n.1(89), 2019/

Finite 2-groups with a non-Dedekind non-metacyclic norm of Abelian non-cyclic subgroups

Authors: Fedir Lyman, Tetyana Lukashova, Marina Drushlyak

Abstract

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.

Fedir Lyman
Herasyma Kondratieva, 134, ap. 64, Sumy, 40021, Ukraine
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Tetyana Lukashova
Kotlyarevskoho, 2/7, ap.1, Sumy, 40013, Ukraine
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Marina Drushlyak
Lysenko, 12, ap.71, Sumy, 40013, Ukraine
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