We offer a comprehensive line of factory automation solutions. Solutions include robots, automation platforms, sequence controllers, human-machine interfaces, variable frequency drives, servo amplifiers and motors, motion controllers, computer numerical control, PC-based CNC, linear servos, and industrial sewing machines, for a broad range of factory automation applications. Free groups - University of Nebraska–Lincoln Free groups Contents 1 Free groups 1 X¡1 = fx ¡1jx 2 Xg; where x¡1 This corollary allows us to identify a free group freely generated by X with the group F(X). In what follows we usually refer to the group F(X) as to a free group on X. Digression. Deflning various free objects (groups, rings, etc.) via their