Finite 2-groups with a non-Dedekind non-metacyclic norm of Abelian non-cyclic subgroups
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2020-10-28 12:31
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512.542+512.544 (1)
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LYMAN, Fedir, LUKASHOVA, Tetyana, DRUSHLYAK, Marina. Finite 2-groups with a non-Dedekind non-metacyclic norm of Abelian non-cyclic subgroups. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2019, nr. 1(89), pp. 3-19. ISSN 1024-7696.
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
Numărul 1(89) / 2019 / ISSN 1024-7696 /ISSNe 2587-4322

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

CZU: 512.542+512.544
MSC 2010: 20D25.

Pag. 3-19

Lyman Fedir, Lukashova Tetyana, Drushlyak Marina
 
Necunoscută, Ucraina
 
 
Disponibil în IBN: 16 august 2019


Rezumat

The authors study finite 2-groups with non-Dedekind non-metacyclic norm NAG of Abelian non-cyclic subgroups depending on the cyclicness or the noncyclicness of the center of a group G. The norm NAG 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.

Cuvinte-cheie
finite group, Non-, Dedekind group, non-metacyclic group, norm of group, norm of, Abelian non-cyclic subgroups.