Lattices of composition formations of finite groups and the laws
Aleksandr Tsarev, Nikolay Nikolayevich Vorob'ev · Journal of Algebra and Its Applications · 2017
We prove that every law of the lattice of all [Formula: see text]-closed formations of finite groups is fulfilled in the lattice of all [Formula: see text]-closed [Formula: see text]-multiply [Formula: see text]-composition formations of finite groups for every non-empty set of primes [Formula: see text] and every non-negative integer [Formula: see text]. Let [Formula: see text] and [Formula: see text] be an infinite set of primes. It is proved that the lattice of all [Formula: see text]-closed [Formula: see text]-multiply [Formula: see text]-composition formations is not distributive.