An infinite family of 2-groups with mixed Beauville structures

2013/04/16 by Nathan Barker, Barker, Nathan, Nigel Boston +5
Mathematics · #14J25 14H30 20F34 #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #math.AG #math.GR #msc:14H30 #msc:14J25 #msc:20F34

paper · pdf · doi:10.48550/arxiv.1304.4480

18 pages

arxiv created 2013/04/16 · arxiv updated 2013/04/17

Abstract

We construct an infinite family of triples (G_k,H_k,T_k), where G_k are 2-groups of increasing order, H_k are index-2 subgroups of G_k, and T_k are pairs of generators of H_k. We show that the triples u_k = (G_k,H_k,T_k) are mixed Beauville structures if k is not a power of 2. This is the first known infinite family of 2-groups admitting mixed Beauville structures. Moreover, the associated Beauville surface S(u₃) is real and, for k > 3 not a power of 2, the Beauville surface S(u_k) is not biholomorphic to S(u_k).

Related

• New Examples of Mixed Beauville Groups
• Some Exceptional Beauville Structures
• Beauville surfaces and finite groups
• Generation of finite simple groups with an application to groups acting on Beauville surfaces
• Beauville structures for quotients of generalised GGS-groups