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We prove that every locally finite, congruence modular, minimal variety is minimal as a quasivariety. We also construct all finite, strictly simple algebras generating a congruence distributive variety, such that the set of unary term operations forms a group. Lastly, these results are applied to a problem in algebraic logic to give a sufficient condition for a deductive system to be structurally complete. 1980 Mathematics subject classification (Amer. Math. Soc.) (1985 Revision): 08 B 15, 08 Cdoi:10.1017/s1446788700035266 fatcat:ejxakzfbrzhb3nljv3uvyfdaiq