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Izvorni znanstveni članak
https://doi.org/10.3336/gm.42.2.08

Cyclic subgroups of order 4 in finite 2-groups

Zvonimir Janko ; Mathematical Institute, University of Heidelberg, 69120 Heidelberg, Germany

Puni tekst: engleski, pdf (148 KB) str. 345-355 preuzimanja: 478* citiraj
APA 6th Edition
Janko, Z. (2007). Cyclic subgroups of order 4 in finite 2-groups. Glasnik matematički, 42 (2), 345-355. https://doi.org/10.3336/gm.42.2.08
MLA 8th Edition
Janko, Zvonimir. "Cyclic subgroups of order 4 in finite 2-groups." Glasnik matematički, vol. 42, br. 2, 2007, str. 345-355. https://doi.org/10.3336/gm.42.2.08. Citirano 17.10.2021.
Chicago 17th Edition
Janko, Zvonimir. "Cyclic subgroups of order 4 in finite 2-groups." Glasnik matematički 42, br. 2 (2007): 345-355. https://doi.org/10.3336/gm.42.2.08
Harvard
Janko, Z. (2007). 'Cyclic subgroups of order 4 in finite 2-groups', Glasnik matematički, 42(2), str. 345-355. https://doi.org/10.3336/gm.42.2.08
Vancouver
Janko Z. Cyclic subgroups of order 4 in finite 2-groups. Glasnik matematički [Internet]. 2007 [pristupljeno 17.10.2021.];42(2):345-355. https://doi.org/10.3336/gm.42.2.08
IEEE
Z. Janko, "Cyclic subgroups of order 4 in finite 2-groups", Glasnik matematički, vol.42, br. 2, str. 345-355, 2007. [Online]. https://doi.org/10.3336/gm.42.2.08

Sažetak
We determine completely the structure of finite 2-groups which possess exactly six cyclic subgroups of order 4. This is an exceptional case because in a finite 2-group is the number of cyclic subgroups of a given order 2n (n ≥ 2 fixed) divisible by 4 in most cases and this solves a part of a problem stated by Berkovich. In addition, we show that if in a finite 2-group G all cyclic subgroups of order $4$ are conjugate, then G is cyclic or dihedral. This solves a problem stated by Berkovich.

Ključne riječi
Finite 2-groups; 2-groups of maximal class; minimal nonabelian 2-groups; L2-groups; U2-groups

Hrčak ID: 17946

URI
https://hrcak.srce.hr/17946

Posjeta: 733 *