On the structure of $LC$-nilpotent groups

M. Amiri; I. Kashuba; I. Lima

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arXiv · 2212.03104

On the structure of $LC$-nilpotent groups

M. Amiri·I. Kashuba·I. Lima

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Abstract

For a finite group $G$, let $LC(G)$ be the subgroup generated by elements $x$ such that, for all $y \in G$ and all integers $n$, the order of $x^n y$ divides the least common multiple of the orders of $x$ and $y$. This subgroup is a nilpotent characteristic subgroup of $G$. In this article, among other results, we show that a finite solvable group $G$ admits an $LC$-nilpotent series if and only if $G$ does not contain any $2$-Frobenius subgroup of type $(p, q, p)$. As a consequence of this theorem, we conclude that the algebraic system comprising all $LC$-nilpotent groups forms a variety.

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BibTeX RIS

M. Amiri, I. Kashuba, I. Lima. 2026-07-11. On the structure of $LC$-nilpotent groups. https://arxiv.org/abs/2212.03104

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