• On 𝐴-nilpotent abelian groups

• # Fulltext

https://www.ias.ac.in/article/fulltext/pmsc/124/04/0517-0525

• # Keywords

Automorphism; lower autocentral series; abelian groups.

• # Abstract

Let 𝐺 be a group and $A = \text{Aut}(G)$ be the group of automorphisms of 𝐺. Then, the element $[g, \alpha] = g^{-1}\alpha(g)$ is an autocommutator of $g \in G$ and $\alpha \in A$. Hence, for any natural number 𝑚 the 𝑚-th autocommutator subgroup of 𝐺 is defined as

$K_{m}(G)=\langle [g,\alpha_{1},\ldots,\alpha_{m}]|g\in G,\alpha_{1},\ldots,\alpha_{m}\in A\rangle$,

where $[g, \alpha_{1}, \alpha_{2},\ldots, \alpha_{m}] = [[g,\alpha_{1},\ldots,\alpha_{m−1}], \alpha_{m}]$. In this paper, we introduce the new notion of 𝐴-nilpotent groups and classify all abelian groups which are 𝐴-nilpotent groups.

• # Author Affiliations

1. Department of Mathematics, University of Birjand, Birjand, Iran

• # Proceedings – Mathematical Sciences

Current Issue
Volume 129 | Issue 3
June 2019