Group Embeddings of Configurations with Prover9 Eric Ens and R. Padmanabhan A configuration is a finite set of elements (called "points" just to have a guiding analogy with the plane geometry) and a finite set of blocks (again, we call them "lines") such that each point is incident with the same number of lines and each line is incident with same number of points. The most well-known examples of configurations are the 7-point Fano configuration, the 9-point configuration of inflection points on a complex cubic and the 10-point Desargues configuration. This topic was popularized by Hilbert and Cohn-Vossen in their celebrated book Anschauliche Geometry (reprinted in English as Geometry and Imagination). Motivated by the geometric definition of a group law on non-singular cubic curves, we define the concept of group embeddability of (n, k) configurations and classify the set of all (11, 3) s which can be embedded into abelian groups in such a way that if {P,Q,R} is a line in the configuration then P+Q+R = 0 in the abelian group. We apply these results to their geometric realizability (over a projective plane). Naturally, there are two kinds of theorems we need to prove: for a given configuration, we have either a concrete group representation or else a proof that no such representation exists. Prover9 is successfully employed to get the proofs of both kinds.