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Fully-diverse constellations, i.e., a set of unitary matrices whose pairwise differences are nonsingular, are useful in multiantenna communications especially in multiantenna differential modulation, since they have good pairwise error properties. Recently, group theoretic ideas, especially fixed-point-free (fpf) groups, have been used to design fully-diverse constellations of unitary matrices. Here we give systematic methods to design space-time codes which are appropriate for three-transmit-antenna differential modulation. The structures of the codes are motivated by the Lie group SU(3). One of the codes, called the AB code, has a fast decoding algorithm using the complex sphere decoder. The diversity products of the codes can be easily calculated and simulated performances show that the codes are better than the group-based codes (A. Shokrollahi, et al., 2001) especially at high rates and as good as the elaborately-designed nongroup codes (A. Shokrollahi, et al., 2001).