3,241 research outputs found
New Beauville surfaces and finite simple groups
In this paper we construct new Beauville surfaces with group either
\PSL(2,p^e), or belonging to some other families of finite simple groups of
Lie type of low Lie rank, or an alternating group, or a symmetric group,
proving a conjecture of Bauer, Catanese and Grunewald. The proofs rely on
probabilistic group theoretical results of Liebeck and Shalev, on classical
results of Macbeath and on recent results of Marion.Comment: v4: 18 pages. Final version, to appear in Manuscripta Mat
Some Exceptional Beauville Structures
We first show that every quasisimple sporadic group possesses an unmixed
strongly real Beauville structure aside from the Mathieu groups M11 and M23
(and possibly 2B and M). We go on to show that no almost simple sporadic group
possesses a mixed Beauville structure. We then go on to use the exceptional
nature of the alternating group A6 to give a strongly real Beauville structure
for this group explicitly correcting an earlier error of Fuertes and
Gonzalez-Diez. In doing so we complete the classification of alternating groups
that possess strongly real Beauville structures. We conclude by discussing
mixed Beauville structures of the groups A6:2 and A6:2^2.Comment: v4 - case Co2 ammende
Series of -groups with Beauville structure
For every we show that each finite -group with an unmixed
Beauville structure is part of a surjective infinite projective system of
finite -groups with compatible unmixed Beauville structures. This leads to
the new notion of an unmixed topological Beauville structure on pro-finite
groups. We further construct for a new explicit infinite series of
non-abelian -groups that allow unmixed Beauville structures.Comment: 7 pages, to appear in: Monatshefte der Mathemati
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