The Best Extending Cover-preserving Geometric Lattices of Semimodular Lattices

In 2010, Gábor Czédli and E. Tamás Schmidt mentioned that the best cover-preserving embedding of a given semimodular lattice is not known yet [A lattices into geometric lattices. Advances in Mathematics, 225, 2455–2463 (2010)]. That to say: What are G such finite L has with smallest ∣G∣? this paper, we propose an algorithm calculate all extending prove length number atoms every equal non-zero join-irreducible elements L, respectively. Therefore, solve problem on raised by Schmidt.