Geodesic
On subgroups of finite exponent in groups
Algebra and discrete mathematics, Tome 19 (2015) no. 1, pp. 1-7

Voir la notice de l'article provenant de la source Math-Net.Ru

We investigate properties of groups with subgroups of finite exponent and prove that a non-perfect group $G$ of infinite exponent with all proper subgroups of finite exponent has the following properties: $(1)$ $G$ is an indecomposable $p$-group, $(2)$ if the derived subgroup $G'$ is non-perfect, then $G/G''$ is a group of Heineken-Mohamed type. We also prove that a non-perfect indecomposable group $G$ with the non-perfect locally nilpotent derived subgroup $G'$ is a locally finite $p$-group.
Keywords: locally finite group, finitely generated group, exponent, group of Heineken-Mohamed type. 
@article{ADM_2015_19_1_a1,
     author = {Orest D. Artemovych},
     title = {On subgroups of finite exponent in groups},
     journal = {Algebra and discrete mathematics},
     pages = {1--7},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2015_19_1_a1/}
}
TY  - JOUR
AU  - Orest D. Artemovych
TI  - On subgroups of finite exponent in groups
JO  - Algebra and discrete mathematics
PY  - 2015
SP  - 1
EP  - 7
VL  - 19
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2015_19_1_a1/
LA  - en
ID  - ADM_2015_19_1_a1
ER  - 
%0 Journal Article
%A Orest D. Artemovych
%T On subgroups of finite exponent in groups
%J Algebra and discrete mathematics
%D 2015
%P 1-7
%V 19
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2015_19_1_a1/
%G en
%F ADM_2015_19_1_a1
Orest D. Artemovych. On subgroups of finite exponent in groups. Algebra and discrete mathematics, Tome 19 (2015) no. 1, pp. 1-7. http://geodesic.mathdoc.fr/item/ADM_2015_19_1_a1/