#### Glasnik Matematicki, Vol. 40, No.2 (2005), 235-240.

### FINITE *p*-GROUPS WITH A UNIQUENESS CONDITION
FOR NON-NORMAL SUBGROUPS

### Zvonimir Janko

Mathematical Institute, University of Heidelberg,
69120 Heidelberg, Germany

*e-mail:* `janko@mathi.uni-heidelberg.de`

**Abstract.** We determine up to isomorphism all finite
*p*-groups *G* which possess non-normal subgroups and each
non-normal subgroup is contained in exactly one maximal subgroup
of *G*. For *p* = 2 this problem was essentially more difficult and
we obtain in that case two new infinite families of finite
2-groups.

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

**Key words and phrases.** Finite *p*-groups, minimal nonabelian
*p*-groups, 2-groups of maximal class, Hamiltonian groups.

**Full text (PDF)** (free access)
DOI: 10.3336/gm.40.2.04

**References:**

- B. Huppert,
Endliche Gruppen 1, Springer, Berlin, 1967.

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