An Infinite Family of 2-Groups with Mixed Beauville Structures

We construct an infinite family of triples (Gk,Hk,Tk), where Gk are 2-groups of increasing order, Hk are index 2 subgroups of Gk, and Tk are pairs of generators of Hk. We show that the triples uk=(Gk,Hk,Tk) 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(uk) is not biholomorphic to $\overline {S(u_k)}$.