Glasnik matematički, Vol. 42 No. 2, 2007.
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
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
Datum izdavanja:
11.12.2007.
Posjeta: 1.506 *