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Overgroups of order 2n additive regular groups of a residue ring and of a vector space

  • Boris A. Pogorelov EMAIL logo and Marina A. Pudovkina EMAIL logo
Published/Copyright: August 22, 2016
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Discrete Mathematics and Applications
From the journal Discrete Mathematics and Applications Volume 26 Issue 4

Abstract

The additive groups of the residue ring ℤ2n and of the vector space Vn over the field GF(2), as well as the group Gn generated by these additive groups, share common imprimitivity systems and enter as subgroups into the Sylow 2-subgroup of the symmetric group S(ℤ2n). These groups are used in cryptography as an encryption tool with the operations of addition in Vn and ℤ2n. The permutation structure of the subgroups of the group Gn is presented. The kernels of homomorphisms which correspond to various systems of imprimitivity, the normal subgroups, and some modular representations of the group Gn 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

Originally published in Diskretnaya Matematika (2016)27, No3, 74–94 (in Russian).

References

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Received: 2014-12-26
Published Online: 2016-8-22
Published in Print: 2016-8-1

© 2016 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/dma-2016-0021
Keywords for this article
wreath product of permutation groups; imprimitive group; Sylow 2-subgroup; additive group of the residue ring; additive group of the vector space

Articles in the same Issue

  1. Frontmatter
  2. Research Article
  3. Characterization of almost perfect nonlinear functions in terms of subfunctions
  4. Research Article
  5. Estimates for distribution of the minimal distance of a random linear code
  6. Research Article
  7. The distributions of interrecord fillings
  8. Research Article
  9. Galois theory for clones and superclones
  10. Research Article
  11. Overgroups of order 2n additive regular groups of a residue ring and of a vector space
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