Proof of a conjecture of Wiegold for nilpotent Lie algebras. (December 2020)

• Record Type: Journal Article
• Authors: Skutin, A. A.
• Is Part Of: Sbornik. Volume 211:Number 12(2020)
• Page Start: 1795
• Page End: 1800
• Publication Date: 2020-12
• Subjects: 17B20; 17B50; nilpotent Lie algebras -- finite $p$-groups -- breadth of an element -- estimate for the size of the commutator subalgebra; Mathematics -- Periodicals; 510.5
• DOI: 10.1070/SM9350
• Languages: English
• ISSNs: 1064-5616

Abstract

Abstract: Let be a nilpotent Lie algebra. By the breadth of an element of we mean the number . Vaughan-Lee showed that if the breadth of all elements of the Lie algebra is bounded by a number, then the dimension of the commutator subalgebra of the Lie algebra does not exceed . We show that if for some nonnegative, then the Lie algebra is generated by the elements of breadth, and thus we prove a conjecture due to Wiegold (Question 4.69 in the Kourovka Notebook) in the case of nilpotent Lie algebras. Bibliography: 4 titles.