Original scientific paper

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

Abstract

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.

Keywords

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

Publication date:

11.12.2007.

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