#### Glasnik Matematicki, Vol. 40, No.1 (2005), 59-69.

### SECOND-METACYCLIC FINITE 2-GROUPS

### Vladimir Cepulic, Marijana Ivankovic and
Elizabeta Kovac 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`

*e-mail:* `marijana.ivankovic@fer.hr`
Department of Mathematics, Faculty of Transport and Traffic
Engineering, University of Zagreb, Vukeliceva 4, HR-10000 Zagreb,
Croatia

**Abstract.** Second-metacyclic finite 2-groups are finite
2-groups with some non-metacyclic maximal subgroup and with all
second-maximal subgroups being metacyclic. According to a known result
there are only four non-metacyclic finite 2-groups with all maximal
subgroups being metacyclic. The groups pointed in the title should
contain some of these groups as a subgroup of index 2. There are
seventeen second-maximal finite 2-groups, four among them being of
order 16, ten of order 32 and three of order 64.

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

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

**Full text (PDF)** (free access)
DOI: 10.3336/gm.40.1.07

**References:**

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

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