Geodesic
Overgroups of order ${2^n}$ additive regular groups of a residue ring and of a vector space
Diskretnaya Matematika, Tome 27 (2015) no. 3, pp. 74-94

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The additive groups of the residue ring ${\mathbb{Z}_{{2^n}}}$ and of the vector space ${V_n}$ over the field $GF(2)$, as well as the group ${G_n}$ generated by these additive groups, share common imprimitivity systems and enter as subgroups into the Sylow 2-subgroup of the symmetric group $S({\mathbb{Z}_{{2^n}}})$. These groups are used in cryptography as an encryption tool with the operations of addition in ${V_n}$ and ${\mathbb{Z}_{{2^n}}}$. The permutation structure of the subgroups of the group ${G_n}$ is presented. The kernels of homomorphisms which correspond to various systems of imprimitivity, the normal subgroups, and some modular representations of the group ${G_n}$ over the field $GF(2)$ are described.
Keywords: wreath product of permutation groups, imprimitive group, Sylow 2-subgroup, additive group of the residue ring, additive group of the vector space. 
@article{DM_2015_27_3_a5,
     author = {B. A. Pogorelov and M. A. Pudovkina},
     title = {Overgroups of order ${2^n}$ additive regular groups of a residue ring and of a vector space},
     journal = {Diskretnaya Matematika},
     pages = {74--94},
     publisher = {mathdoc},
     volume = {27},
     number = {3},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2015_27_3_a5/}
}
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B. A. Pogorelov; M. A. Pudovkina. Overgroups of order ${2^n}$ additive regular groups of a residue ring and of a vector space. Diskretnaya Matematika, Tome 27 (2015) no. 3, pp. 74-94. http://geodesic.mathdoc.fr/item/DM_2015_27_3_a5/