Geodesic
Every $2$-group with all subgroups normal-by-finite is locally finite
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 2, pp. 491-496

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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 $| H/H_{G} | \leq 2$ for every subgroup $H$ of $G$, then $G$ contains an Abelian subgroup of index at most $8$.
DOI : 10.21136/CMJ.2018.0504-16
Classification : 20D15, 20F14, 20F50
Keywords: $2$-group; locally finite group; normal-by-finite subgroup; core-finite group 
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Jabara, Enrico. Every $2$-group with all subgroups normal-by-finite is locally finite. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 2, pp. 491-496. doi: 10.21136/CMJ.2018.0504-16

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