#### Glasnik Matematicki, Vol. 46, No.1 (2011), 71-77.

### ON FINITE *p*-GROUPS CONTAINING A MAXIMAL ELEMENTARY ABELIAN SUBGROUP OF ORDER *p*^{2}

### Yakov Berkovich

Department of Mathematics,
University of Haifa,
Mount Carmel, Haifa 31905,
Israel

**Abstract.** We continue investigation
of a *p*-group *G* containing a maximal
elementary abelian subgroup *R* of order *p*^{2},
*p>2*, initiated by Glauberman and Mazza [6];
case *p=2* also considered. We study the
structure of the centralizer of *R* in *G*.
This reduces the investigation of the
structure of *G* to results of Blackburn and
Janko (see references). Minimal nonabelian
subgroups play important role in proofs of
Theorems 2 and 5.

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

**Key words and phrases.** Minimal nonabelian *p*-group,
maximal elementary abelian subgroup, soft subgroup.

**Full text (PDF)** (access from subscribing institutions only)
DOI: 10.3336/gm.46.1.09

**References:**

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

MathSciNet

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

MathSciNet

- Y. Berkovich and Z. Janko, Groups of
prime power order. Vol. 3, Walter de Gruyter,
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- N. Blackburn,
*Generalizations of certain
elementary theorems on **p*-groups, Proc. London
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MathSciNet
CrossRef

- N. Blackburn,
*Groups of prime-power
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**(r,1)*, Monatsh. Math. **99** (1985), 1-18.

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CrossRef

- G. Glauberman and N. Mazza,
*p*-groups
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CrossRef

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- Z. Janko,
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CrossRef

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*Finite **2*-groups with small
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MathSciNet
CrossRef

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