There is proved that a convex maximal line in a median group $G$, containing 0, is a direct factor of $G$.
@article{107437,
author = {Milan Kolibiar},
title = {Convex lines in median groups},
journal = {Archivum Mathematicum},
volume = {028},
year = {1992},
pages = {67-75},
zbl = {0783.20038},
mrnumber = {1201867},
language = {en},
url = {http://dml.mathdoc.fr/item/107437}
}
Kolibiar, Milan. Convex lines in median groups. Archivum Mathematicum, Tome 028 (1992) pp. 67-75. http://gdmltest.u-ga.fr/item/107437/
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