#### Glasnik Matematicki, Vol. 41, No.1 (2006), 65-70.

### A CLASS OF NONABELIAN NONMETACYCLIC FINITE 2-GROUPS

### Vladimir Ćepulić and Olga S. Pyliavska

Department of Mathematics, Faculty of Electrical Engineering and Computing,
University of Zagreb, Unska 3, HR-10000 Zagreb, Croatia

*e-mail:* `vladimir.cepulic@fer.hr`
Department of Mathematics, Faculty of Informatics, National University of Kyiv-Mohyla Academy,
vul. Skorovody 2, 0470 Kyiv, Ukraine

**Abstract.** Nonabelian nonmetacyclic finite 2-groups in which every
proper subgroup is abelian or metacyclic and possessing at least
one nonabelian and at least one nonmetacyclic proper subgroup have
been investigated and classified. Using the obtained result and
two previously known results one gets the complete classification
of all nonabelian nonmetacyclic finite 2-groups in which every
proper subgroup is abelian or metacyclic.

**2000 Mathematics Subject Classification.**
20D15.

**Key words and phrases.** Finite group, 2-group, abelian, metacyclic.

**Full text (PDF)** (free access)
DOI: 10.3336/gm.41.1.06

**References:**

- Z. Janko,
*Finite 2-groups with exactly four cyclic subgroups of order 2*^{n},
J. Reine Angew. Math. **566** (2004), 135-181.

MathSciNet
CrossRef

- G. A. Miller and H. Moreno,
*Nonabelian groups in which every subgroup is abelian*,
Trans. Am. Math. Soc. **4** (1903), 398-404.

MathSciNet
CrossRef

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