The order of the product of two elements in the periodic groups. Issue 8 (3rd August 2022) - Amiri, Mohsen; Lima, Igor
Abstract: Let G be a periodic group, and let LCM ( G ) be the set of all x ∈ G such that o ( x n z ) divides the least common multiple of o ( x n ) and o ( z ) for all z in G and all integers n . In this paper, we prove that the subgroup generated by LCM ( G ) is a locally nilpotent characteristic subgroup of G whenever G is a locally finite group.