#### Glasnik Matematicki, Vol. 52, No. 1 (2017), 99-105.

### FINITE NONABELIAN *p*-GROUPS OF EXPONENT *>p* WITH A SMALL NUMBER OF MAXIMAL ABELIAN SUBGROUPS
OF EXPONENT *>p*

### Zvonimir Janko

Mathematical Institute,
University of Heidelberg,
69120 Heidelberg,
Germany

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

**Abstract.**
Y. Berkovich has proposed to classify nonabelian finite *p*-groups *G* of exponent *>p* which have exactly
*p* maximal abelian subgroups of exponent *>p* and this was done here in Theorem 1 for *p=2* and in
Theorem 2 for *p>2*. The next critical case, where *G* has exactly *p+1* maximal abelian subgroups of
exponent *>p* was done only for the case *p=2* in Theorem 3.

**2010 Mathematics Subject Classification.**
20D15.

**Key words and phrases.** Finite *p*-groups, minimal nonabelian subgroups,
maximal abelian subgroups, quasidihedral *2*-groups, Hughes subgroup.

**Full text (PDF)** (access from subscribing institutions only)
DOI: 10.3336/gm.52.1.07

**References:**

- Y. Berkovich,
Groups of prime power order, Vol. 1,
Walter de Gruyter, Berlin-New York, 2008.

MathSciNet
CrossRef

- Y. Berkovich and Z. Janko,
Groups of prime power order, Vol. 2,
Walter de Gruyter, Berlin-New York, 2008.

MathSciNet

- Z. Janko,
*Finite **p*-groups with some isolated subgroups, J. Algebra **465** (2016), 41-61.

MathSciNet
CrossRef

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