Lucchini–Detomi's monolithicity conjecture for sigma-elementary groups
Let GGG be a group with finite covering number … sigma(G)isthesmallestnumberofpropersubgroupsneededtocoveris the smallest number of proper subgroups needed to coveristhesmallestnumberofpropersubgroupsneededtocoverG.Call. Call .CallG………sigma(G)<σ(G/N)…σ\sigma(G/N) … \sigmaσ(G/N)…σ-elementary grou…