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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