Overgroups of order 2 n additive regular groups of a residue ring and of a vector space
Boris Aleksandrovich Pogorelov, Марина Александровна Пудовкина · Discrete Mathematics and Applications · 2016
Abstract The additive groups of the residue ring 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 (ℤ 2 n ). These groups are used in cryptography as an encryption tool with the operations of addition in V n and 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.