Semisymmetric elementary abelian covers of the Möbius-Kantor graph

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Let ₙ → X be a regular covering projection of connected graphs with the group of covering transformations isomorphic to N. If N is an elementary abelian p-group, then the projection ₙ is called p-elementary abelian. The projection ₙ is vertex-transitive (edge-transitive) if some vertex-transitive (edge-transitive) subgroup of X lifts along ₙ, and semisymmetric if it is edge- but not vertex-transitive. The projection ₙ is minimal semisymmetric if pₙ cannot be written as a composition ₙ = ∘ ₘ of two (nontrivial) regular covering projections, where ₘ is semisymmetric. Finding elementary abelian covering projections can be grasped combinatorially via a linear representation of automorphisms acting on the first homology group of the graph. The method essentially reduces to finding invariant subspaces of matrix groups over prime fields (see J. Algebr. Combin., 20 (2004), 71--97). In this paper, all pairwise nonisomorphic minimal semisymmetric elementary abelian regular covering projections of the Möbius-Kantor graph, the Generalized Petersen graph (8,3), are constructed. No such covers exist for p =2. Otherwise, the number of such covering projections is equal to (p-1)/4 and 1+ (p-1)/4 in cases p ≡ 5,9,13,17,21 (24) and p ≡ 1 (24), respectively, and to (p+1)/4 and 1+ (p+1)/4 in cases p ≡ 3,7,11,15,23 (24) and p ≡ 19 (24), respectively. For each such covering projection the voltage rules generating the corresponding covers are displayed explicitly.