On 𝐴-nilpotent abelian groups

Proceedings Mathematical Sciences

Mohammad Mehdi Nasrabadi²  Ali Gholamian¹ 

[1] $$;Department of Mathematics, University of Birjand, Birjand, Iran$$

关键词: Automorphism;    lower autocentral series;    abelian groups.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Let 𝐺 be a group and $A = ext{Aut}(G)$ be the group of automorphisms of 𝐺. Then, the element $[g, 𝛼] = g^{-1}𝛼(g)$ is an autocommutator of $g in G$ and $𝛼 in A$. Hence, for any natural number 𝑚 the 𝑚-th autocommutator subgroup of 𝐺 is defined as$K_{m}(G)=langle [g,𝛼_{1},ldots,𝛼_{m}]|gin G,𝛼_{1},ldots,𝛼_{m}in Aangle$,where $[g, 𝛼_{1}, 𝛼_{2},ldots, 𝛼_{m}] = [[g,𝛼_{1},ldots,𝛼_{m−1}], 𝛼_{m}]$. In this paper, we introduce the new notion of 𝐴-nilpotent groups and classify all abelian groups which are 𝐴-nilpotent groups.

【 授权许可】

Unknown