Influence of minimal subgroups on the product of smooth groups
Keywords:Permutable subgroups, Smooth groups, Subgroup lattices.
A maximal chain in a finite lattice L is called smooth if any two intervals of the same length are isomorphic. We say that a finite group G is totally smooth if all maximal chains in its subgroup lattice L(G) are smooth. In this article, we study the product of finite groups which have a permutable subgroup of prime order under the assumption that the maximal subgroups are totally smooth.
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