Cyclic Subgroups of Order 4 in Finite 2 - Groups
نویسندگان
چکیده
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.
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