We show that a barely transitive group is totally imprimitive if and only if it is locally graded. Moreover, we obtain the description of a barely transitive group G for the case G has a cyclic subgroup 〈x〉 which intersects non-trivially with all subgroups and for the case a point stabilizer H of G has a subgroup H 1 of finite index in H satisfying the identity χ(H 1) = 1, where χ is a multi-linear commutator of weight w.
@article{bwmeta1.element.doi-10_2478_s11533-013-0240-x,
author = {Cansu Betin and Mahmut Kuzucuo\u glu},
title = {On locally graded barely transitive groups},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {1188-1196},
zbl = {1279.20001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0240-x}
}
Cansu Betin; Mahmut Kuzucuoğlu. On locally graded barely transitive groups. Open Mathematics, Tome 11 (2013) pp. 1188-1196. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0240-x/
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