Every -group with all subgroups normal-by-finite is locally finite
Czechoslovak Mathematical Journal (2018)
- Volume: 68, Issue: 2, page 491-496
- ISSN: 0011-4642
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topJabara, Enrico. "Every $2$-group with all subgroups normal-by-finite is locally finite." Czechoslovak Mathematical Journal 68.2 (2018): 491-496. <http://eudml.org/doc/294251>.
@article{Jabara2018,
abstract = {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 $| H/H_\{G\} | \le 2$ for every subgroup $H$ of $G$, then $G$ contains an Abelian subgroup of index at most $8$.},
author = {Jabara, Enrico},
journal = {Czechoslovak Mathematical Journal},
keywords = {$2$-group; locally finite group; normal-by-finite subgroup; core-finite group},
language = {eng},
number = {2},
pages = {491-496},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Every $2$-group with all subgroups normal-by-finite is locally finite},
url = {http://eudml.org/doc/294251},
volume = {68},
year = {2018},
}
TY - JOUR
AU - Jabara, Enrico
TI - Every $2$-group with all subgroups normal-by-finite is locally finite
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 2
SP - 491
EP - 496
AB - 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 $| H/H_{G} | \le 2$ for every subgroup $H$ of $G$, then $G$ contains an Abelian subgroup of index at most $8$.
LA - eng
KW - $2$-group; locally finite group; normal-by-finite subgroup; core-finite group
UR - http://eudml.org/doc/294251
ER -
References
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