## Experimental Mathematics

- Experiment. Math.
- Volume 21, Issue 3 (2012), 298-306.

### A Note on Beauville $p$-Groups

Nathan Barker, Nigel Boston, and Ben Fairbairn

#### Abstract

We examine which $p$-groups of order $\le p^6$ are Beauville. We completely classify them for groups of order $\le p^4$. We also show that the proportion of 2-generated groups of order $p^5$ that are Beauville tends to 1 as $p$ tends to infinity; this is not true, however, for groups of order $p^6$. For each prime $p$ we determine the smallest nonabelian Beauville $p$-group.

#### Article information

**Source**

Experiment. Math., Volume 21, Issue 3 (2012), 298-306.

**Dates**

First available in Project Euclid: 13 September 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1347541279

**Mathematical Reviews number (MathSciNet)**

MR2988581

**Zentralblatt MATH identifier**

1259.20016

**Subjects**

Primary: 14J29: Surfaces of general type 20D15: Nilpotent groups, $p$-groups 20E34: General structure theorems 30F10: Compact Riemann surfaces and uniformization [See also 14H15, 32G15]

**Keywords**

Beauville structure Beauville group $p$-groups Beauville surface

#### Citation

Barker, Nathan; Boston, Nigel; Fairbairn, Ben. A Note on Beauville $p$-Groups. Experiment. Math. 21 (2012), no. 3, 298--306. https://projecteuclid.org/euclid.em/1347541279