  In 1985, Arjeh Cohen and Jacques Tits proved the existence of a 4-cycle-free
2-fold cover of the hypercube. This Cohen-Tits cover is closely related to the
signed adjacency matrix that Hao Huang used last year in his proof of the
Sensitivity Conjecture. Terence Tao observed that Huang's signed adjacency
matrix can be understood by lifting functions on an elementary abelian 2-group
to functions on a central extension. Inspired by Tao's observation, we
generalize the Cohen-Tits cover by constructing, as Cayley graphs for
extraspecial p-groups, two infinite families of 4-cycle-free p-fold covers of
the Cartesian product of p-cycles.
