A communicator station wirelessly transmits frames to and receives frames from a least one additional communicator in a Group in accordance with a MAC protocol. One of the communicators functions as a hub and the remaining communicators function as remotes. The hub sends control information to the hubs to establish repeating communication cycles, each of which has intervals during which the hub and the remotes transmit and receive frames. The intervals allow the hub and the remotes to anticipate transmitting and receiving frames, thereby allowing the remotes to power off their receivers and transmitters to achieve a considerable savings in power consumption without degrading communications. Other improved features include adjusting the intervals and the durations of transmission opportunities in the communication cycle to obtain the beneficial aspects of TDMA and PRMA for LAN-like communication without also incurring most of the undesirable aspects of such MAC techniques. Other control functions such as arbitration determine which communicator is better suited to act as the hub.