A FAMILY OF 2-GROUPS AND AN ASSOCIATED FAMILY OF SEMISYMMETRIC, LOCALLY 2-ARC-TRANSITIVE GRAPHS

. A mixed dihedral group is a group H with two disjoint subgroups X and Y, each elementary abelian of order 2n, such that H is generated by X boolean OR Y, and H/H ' similar to= X x Y. In this paper, for each n >= 2, we construct a mixed dihedral 2-group H of nilpotency class 3 and order 2a where a = (n3 + n2 + 4n)/2, and a corresponding graph sigma, which is the clique graph of a Cayley graph of H. We prove that sigma is semisymmetric, that is, Aut(sigma) acts transitively on the edges but intransitively on the vertices of sigma. These graphs are the first known semisymmetric graphs constructed from groups that are not 2-generated (indeed H requires 2n generators). Additionally, we prove that sigma is locally 2-arc-transitive, and is a normal cover of the 'basic' locally 2-arc-transitive graph K2n,2n . As such, the construction of this family of graphs contributes to the investigation of normal covers of prime-power order of basic locally 2-arc-transitive graphs - the 'local' analogue of a question posed by C. H. Li.