Notes on the Finite Lattice Representation Problem
نویسنده
چکیده
Notation and Terminology. Given a finite lattice L, the expression L ∼= [H,G] means “there exist finite groups H < G such that L is isomorphic to the interval {K | H 6 K 6 G} in the subgroup lattice of G.” A group G is called almost simple if G has a normal subgroup S P G which is nonabelian, simple, and has trivial centralizer, CG(S) = (e). If H 6 G, then the core of H in G, denoted coreG(H), is the largest normal subgroup of G contained in H; it is given by coreG(H) = ⋂ g∈G gHg−1. A subgroup H 6 G for which coreG(H) = (e) is called core-free in G.
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تاریخ انتشار 2011