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Peer reviewed
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Pogorelov, Boris A.; Pudovkina, Marina A.
Discrete mathematics and applications, 8/2016, Volume: 26, Issue: 4Journal Article
The additive groups of the residue ring ℤ and of the vector space over the field (2), as well as the group generated by these additive groups, share common imprimitivity systems and enter as subgroups into the Sylow 2-subgroup of the symmetric group (ℤ ). These groups are used in cryptography as an encryption tool with the operations of addition in and ℤ . The permutation structure of the subgroups of the group is presented. The kernels of homomorphisms which correspond to various systems of imprimitivity, the normal subgroups, and some modular representations of the group over the field (2) are described.
