Geodesic
Flag-transitivity criterion for projective linear group defined over a subring of a base skew field
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 64-69

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It is proved that a projective linear group over a subring of a skew field is flag-transitive if and only if the subring is a Bezout domain and its (left and right) fraction sets coincide with the skew field. This result gives answer for Problem 11.70(b) from Kourovka Notebook.
Keywords: flag-transitivity, projective linear group, projective space. 
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     author = {S. A. Zyubin},
     title = {Flag-transitivity criterion for projective linear group defined over a subring of a base skew field},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {64--69},
     publisher = {mathdoc},
     volume = {11},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2014_11_a1/}
}
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S. A. Zyubin. Flag-transitivity criterion for projective linear group defined over a subring of a base skew field. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 64-69. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a1/