On Intervals in Subgroup Lattices of Finite Groups
نویسنده
چکیده
Example 1. Let G be a finite group. Then the set of all subgroups of G, partially ordered by inclusion, is a lattice. For H ≤ G the sublattice OG(H) of overgroups of H in G is the interval sublattice [H,G]. Call such a lattice a finite group interval lattice. There is a well-known open question as to whether every nonempty finite lattice is isomorphic to a finite group interval lattice. See [PP] for motivation for this question, and see [BL] for one possible approach to proving that the question has a negative answer.
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تاریخ انتشار 2008