This paper considers non-blocking optoelectronic networks in which group operations over a set of numbers are executed during the transmission of one number. A method is proposed to execute group operations using photonic units placed at each multiplexer of the network, along with the circuitry of such executive multiplexers. The new possibility of executing group operations, in parallel across these multiplexers for given sets of users, is described, and procedures for their selection are defined. A bit-bybit synchrony theorem of group operations is proven. The possibility of designing a non-blocking electronic system area network for any number of users is presented, as well as the possibility of designing a similar optoelectronic network as a tandem network with optoelectronic switches controlled by their analogs from the electronic network.