Glasnik Matematicki, Vol. 41, No.2 (2006), 275-282.

SECOND-METACYCLIC FINITE p-GROUPS FOR ODD PRIMES

Vladimir Ćepulić, Olga Pyliavska and Elizabeta Kovač Striko

Department of Mathematics, Faculty of Electrical Engineering and Computing, University of Zagreb, Unska 3, HR-10000 Zagreb, Croatia
e-mail: vladimir.cepulic@fer.hr

National University Kyiv-Mohyla Academy, Skorovody 2, Kyiv 04070, Ukraine

Faculty of Transport and Traffic Engineering, University of Zagreb, Vukeliæeva 4, HR-10000 Zagreb, Croatia
e-mail: elizabeta.kovac@fpz.hr

Abstract.   A second-metacyclic finite p-group is a finite p-group which possesses a nonmetacyclic maximal subgroup, but all its subgroups of index p2 are metacyclic. In this article we determine up to isomorphism all second-metacyclic p-groups for odd primes p. There are ten such groups of order p4, for each prime p ≥ 3, and two such groups of order 35.

2000 Mathematics Subject Classification.   20D15.

Key words and phrases.   Finite group, p-group, metacyclic, second-maximal subgroup, second-metacyclic subgroup.

Full text (PDF) (free access)

DOI: 10.3336/gm.41.2.10

References:

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    MathSciNet     CrossRef

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    MathSciNet

  3. B. Huppert, Endliche Gruppen. I, Springer-Verlag, Berlin-New York, 1967.
    MathSciNet
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