Catalyzes the interconversion of L-glutamate and L-beta-glutamate. Does not have L-lysine 2,3-aminomutase activity. L-glutamate = 3-aminopentanedioate kcat is 6.1 sec(-1) with L-glutamate as substrate. Belongs to the radical SAM superfamily. Highly similar to the L-lysine 2,3-aminomutase. However lacks lysyl-binding Asp residues at positions 332 and 369, that are replaced by Lys and Asn residues, respectively (PubMed:17222594).