1. A method of administering group identifiers of processes in a parallel computer, the parallel computer comprising a plurality of compute nodes, the compute nodes coupled for data communications by one or more data communications networks, one or more of the compute nodes executing a set of processes, the set of processes organized in an operational group for collective parallel operations, the method comprising: receiving from a compute node of the plurality of compute nodes, by each process in the set of processes, a request to establish the set of processes as an operational group including receiving a list of process identifiers for each process of the set of processes; and generating, by each process without communication amongst the processes, a unique group identifier in dependence upon the list of process identifiers.