#### 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 *p*^{2} 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 *p*^{4}, for
each prime *p* ≥ 3, and two such groups of order 3^{5}.

**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:**

- N. Blackburn,
*Generalizations of certain elementary theorems on
**p*-groups, Proc. London Math. Soc. (3) **11**
(1961), 1-22.

MathSciNet
CrossRef

- V. Cepulic, M. Ivankovic and E. Kovac Striko,
*Second-metacyclic finite 2-groups*,
Glas. Mat. Ser. III **40(60)** (2005), 59-69.

MathSciNet

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

MathSciNet

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