Glasnik Matematicki, Vol. 42, No.2 (2007), 345-355.
CYCLIC SUBGROUPS OF ORDER 4 IN FINITE 2-GROUPS
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.
2000 Mathematics Subject Classification.
Key words and phrases. Finite 2-groups, 2-groups of maximal class,
minimal nonabelian 2-groups, L2-groups, U2-groups.
Full text (PDF) (free access)
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