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A maximal chain in a finite lattice L is called smooth if any two intervals of the same length are isomorphic. We call a lattice L totally smooth if all maximal chains of L are smooth. The main concept in this paper is that of a generalized smooth group, that is, a group G such that G / H is totally smooth for every subgroup H of G of prime order. The purpose of this paper is to determine the structure of generalized smooth groups.
Forum Mathematicum – de Gruyter
Published: Jan 26, 2006
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