Geodesic
On the group properties of substitutions defined on the subgroup cosets of finite Abelian group of composite order
Matematičeskie voprosy kriptografii, Tome 7 (2016) no. 1, pp. 83-92 
A. Yu. Maksimovskiy. On the group properties of substitutions defined on the subgroup cosets of finite Abelian group of composite order. Matematičeskie voprosy kriptografii, Tome 7 (2016) no. 1, pp. 83-92. http://geodesic.mathdoc.fr/item/MVK_2016_7_1_a4/
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     title = {On the group properties of substitutions defined on the subgroup cosets of finite {Abelian} group of composite order},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2016_7_1_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Necessary and sufficient conditions of transitivity and primitivity of substitution groups generated by substitutions on the cosets of the Abelian group $G$ are obtained. The structure of these groups is described for the case of their primitivity and for the case when $G$ is the direct product of its subgroups. Necessary and sufficient conditions of primitivity of the group generated by the right regular representation of the group $G$ and a substitution defined on the cosets of the group $G$ are obtained also.

[1] Kholl M., Teoriya grupp, Per. s angl. N. V. Dyumina, Z. P. Zhilinskoi, ed. L. A. Kaluzhnin, Izd-vo inostr. lit., M., 1962, 468 pp.