Naslov
Finite 2-groups with exactly four cyclic subgroups of order 2^n

Autori
Janko, Zvonimir

Izvornik
Journal für die Reine und Angewandte Mathematik (0075-4102) I (2004), 566; 135-181

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
finite 2-group; cyclic group; dihedral group; quaternion group; metacyclic group

Sažetak
In this paper finite 2-groups G with exactly four cyclic subgroups of order 2^n(n>=2) (n fixed) are classified. It turns out that these four cyclic subgroups of order 2^n generate always a subgroup of order 2^n+2. In the second part of the paper a kind of converse of this result is proved. If G is a finite 2-group all of whose elements of order 2^n generate a subgroup of order 2^n+2, then the structure of g is completly determined. At the end of the paper we completely classify so called Uˇ2-groups and give a new non-computational proof of the famous Blackburn's theorem in which minimal non-metacyclic 2-groups are completely classified.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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