Strengthened Wiegold Conjecture in the Theory of Nilpotent Lie Algebras

A. A. Skutin

Lomonosov Moscow State University

Abstract: In the present paper, we strengthen the assertion of the Wiegold conjecture for nilpotent Lie algebras over an infinite field by proving that if there exists a subset of a nilpotent Lie algebra $\mathfrak{g}$ consisting of elements of breadth not exceeding $n$ and satisfying some additional conditions, then the dimension of the commutator subalgebra $\mathfrak{g'}$ of $\mathfrak{g}$ does not exceed $n(n+1)/2$.

Keywords: nilpotent Lie algebras, finite $p$-groups, Wiegold conjecture, iterated constructions.

UDC: 512.554.32

Received: 30.09.2021

DOI: 10.4213/mzm13315

 English version: Mathematical Notes, 2022, 111:5, 747–753

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