Experimental Mathematics

A Note on Beauville $p$-Groups

Nathan Barker, Nigel Boston, and Ben Fairbairn

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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


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