Abstract
This paper is concerned with images of cosets in the direct product of groups by bijective mappings from factors to groups.We prove necessary and sufficient conditions on bijective mappings for existence a coset in the direct product of two groups whose image is a coset. Under some constraints on bijective mappings, we describe the cosets in the direct product of groups, whose images by bijective mappings from factors to groups are cosets, We described the cosets in the direct product of elementary abelian 2-groups whose images by the inversion permutation of nonzero elements of a finite field on factors are cosets. We also describe the similar cosets for the permutation used an an s-box of Kuznyechik algorithm, Under some constraints on bijective mappings, we describe the automorphisms of the direct product groups which commute with bijective mappings from factors to groups.
Originally published in Diskretnaya Matematika (2023) 35, №4, 18–45 (in Russian).
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Articles in the same Issue
- Frontmatter
- On cosets in the direct product of groups whose images by bijective mappings from factors to groups are cosets
- On the linear disjunctive decomposition of a p-logic function into a sum of functions
- Hadamard square of series connected linear codes
- New bounds for the nonlinearity of PN functions and APN functions over finite fields
- Describing the closed class of polynomial functions modulo a power of a prime number by a relation
Articles in the same Issue
- Frontmatter
- On cosets in the direct product of groups whose images by bijective mappings from factors to groups are cosets
- On the linear disjunctive decomposition of a p-logic function into a sum of functions
- Hadamard square of series connected linear codes
- New bounds for the nonlinearity of PN functions and APN functions over finite fields
- Describing the closed class of polynomial functions modulo a power of a prime number by a relation