On local formations with complemented local subformations (Q1902835)

We prove the following theorem giving a complete description for local formations with complemented local subformations. Theorem. Let \(\mathfrak F\) be an \(n\)-multiply local formation, \(n\geq 0\). Then the following conditions are equivalent: 1) the lattice of \(n\)-multiply local subformations of the formation \(\mathfrak F\) is Boolean; 2) \({\mathfrak F}=l_n\text{ form }\mathfrak X\), where \(\mathfrak X\) is a certain set of simple groups, in addition, for \(n\geq 1\) all the groups from \(\mathfrak X\) are abelian; 3) in \(\mathfrak F\), being an atom of the lattice of \(n\)-multiply local formations, every subformation is complemented.