A solvable primitive group with finitely generated abelian stabilizers is finite.
@article{118574, author = {K. K. \v S\v cukin}, title = {A note on simple medial quasigroups}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {34}, year = {1993}, pages = {221-222}, zbl = {0787.20002}, mrnumber = {1241730}, language = {en}, url = {http://dml.mathdoc.fr/item/118574} }
Ščukin, K. K. A note on simple medial quasigroups. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 221-222. http://gdmltest.u-ga.fr/item/118574/
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