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A group G is called smooth if its subgroup lattice L(G) has a smooth chain, and we call G totally smooth if all maximal chains in L(G) are smooth. We call G is a minimal non-totally smooth group if G is not totally smooth with totally smooth proper subgroups. In this paper we determine all finite minimal non-totally smooth groups. Mathematics Subject Classification: 20D30, 20E15doi:10.12988/ija.2013.3551 fatcat:k5yde27yqneczlm3xzksvqt5um