On projectively inert subgroups of completely decomposable finite rank groups
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 67 (2020), pp. 63-68
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Let a group $G$ be a finite direct sum of torsion-free rank $1$ groups $G_{i}$. It is proved that every projectively inert subgroup of $G$ is commensurate with a fully invariant subgroup if and only if all $G_{i}$ are not divisible by any prime number $p$, and for different subgroups $G_{i}$ and $G_{j}$ their types are either equal or incomparable.
Keywords:
projectively inert subgroup, fully invariant subgroup, commensurable subgroups, index of the subgroup, completely decomposable group.
@article{VTGU_2020_67_a5,
author = {A. R. Chekhlov and O. V. Ivanets},
title = {On projectively inert subgroups of completely decomposable finite rank groups},
journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
pages = {63--68},
publisher = {mathdoc},
number = {67},
year = {2020},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VTGU_2020_67_a5/}
}
TY - JOUR AU - A. R. Chekhlov AU - O. V. Ivanets TI - On projectively inert subgroups of completely decomposable finite rank groups JO - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika PY - 2020 SP - 63 EP - 68 IS - 67 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VTGU_2020_67_a5/ LA - ru ID - VTGU_2020_67_a5 ER -
%0 Journal Article %A A. R. Chekhlov %A O. V. Ivanets %T On projectively inert subgroups of completely decomposable finite rank groups %J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika %D 2020 %P 63-68 %N 67 %I mathdoc %U http://geodesic.mathdoc.fr/item/VTGU_2020_67_a5/ %G ru %F VTGU_2020_67_a5
A. R. Chekhlov; O. V. Ivanets. On projectively inert subgroups of completely decomposable finite rank groups. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 67 (2020), pp. 63-68. http://geodesic.mathdoc.fr/item/VTGU_2020_67_a5/