Every $2$-group with all subgroups normal-by-finite is locally finite

Czechoslovak Mathematical Journal

Enrico Jabara¹ 

关键词: $2$-group;    locally finite group;    normal-by-finite subgroup;    core-finite group;   

DOI  :  10.21136/CMJ.2018.0504-16

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

  A group $G$ has all of its subgroups normal-by-finite if $H/H_G$ is finite for all subgroups $H$ of $G$. The Tarski-groups provide examples of $p$-groups ($p$ a "large" prime) of nonlocally finite groups in which every subgroup is normal-by-finite. The aim of this paper is to prove that a $2$-group with every subgroup normal-by-finite is locally finite. We also prove that if $| H/H_G | \leq2$ for every subgroup $H$ of $G$, then $G$ contains an Abelian subgroup of index at most $8$.

【 授权许可】

Unknown