Designing a group secret key scheme to secure communication between nodes represents a huge challenge to wireless networks. To address this issue, we propose a group key extraction scheme based on three nodes. In this scheme, we first select a trusted authorization system to group the user nodes in the network. Then we extract the short key with the wireless channel characteristics of the physical layer and exchange the information signed by Schnorr. Finally, we make each user node authenticate its neighboring nodes. If the authentication is passed, a group key is established for the nodes in the network. The simulation results reveal a positive correlation between the group key rate and the signal-to-noise ratio, and the group key rate does not decrease with the increase in the number of nodes. It proves this scheme is applicable to wireless networks.