Cyclic subgroups of order 4 in finite 2-groups | Zendy

Zvonimir Janko | Zendy

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Cyclic subgroups of order 4 in finite 2-groups

Author(s) -

Zvonimir Janko

Publication year - 2007

Publication title -

glasnik matematicki

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.332

H-Index - 17

eISSN - 1846-7989

pISSN - 0017-095X

DOI - 10.3336/gm.42.2.08

Subject(s) - mathematics , order (exchange) , cyclic group , locally finite group , pure mathematics , combinatorics , business , abelian group , finance

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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