A multi-user space-time block coding (STBCa) system is a multi-access system where co-channel users employ space-time block codes (STBC). In this paper, we aimed at the design of efficient zero-forcing (ZF) receivers, especially ZF iterative interference cancellation (IC) receivers, for multi-user {G2, G3, G4} STBC systems with an arbitrary number of users, based on the identification of algebraic properties existing in the systems. First, we identify some algebraic properties for {G2, G3, G4} STBC systems. Then, utilizing these algebraic properties, we further expose two significative properties, called "ZF output uncorrelated property" and "ZF output equal Post-detection SNR property" respectively, for least-squares (LS) ZF receivers in multi-user {G2, G3, G4} STBC systems by detailed proofs. Based on the two properties, a novel LS ZF user-ordered successive interference cancellation (ZF UOSIC) detection algorithm is proposed subsequently. Finally, simulation results show that ZF UOSIC is superior to the conventional ZF IC and maximum-likelihood (ML) algorithms and the non-ordered ZF user-based SIC (ZF USIC) algorithm due to adopting iterative IC and optimal ordering among users, and has very close performance to the ZF symbol-ordered SIC but with lower complexity due to the fewer iterative times.