The order of the product of two elements in the periodic groups. Issue 8 (3rd August 2022)

• Record Type: Journal Article
• Authors: Amiri, Mohsen; Lima, Igor
• Is Part Of: Communications in algebra. Volume 50:Issue 8(2022)
• Page Start: 3473
• Page End: 3480
• Publication Date: 2022-08-03
• Subjects: Nilpotent groups -- periodic groups; 20F50 -- 20F18; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2022.2034836
• Languages: English
• ISSNs: 0092-7872

Abstract

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.