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:

  1. Z. Janko, Finite 2-groups with exactly four cyclic subgroups of order 2n, J. Reine Angew. Math. 566 (2004), 135-181.
    MathSciNet     CrossRef

  2. 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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