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Finite 2-groups with a non-Dedekind non-metacyclic norm of abelian non-cyclic subgroups. (English) Zbl 1452.20013

Summary: 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.

MSC:

20D25 Special subgroups (Frattini, Fitting, etc.)
20D15 Finite nilpotent groups, \(p\)-groups
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References:

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