Generation of the alternating group by modular additions
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Fedor M. Malyshev
Abstract
The paper is concerned with systems of generators of permutation groups on Cartesian products of residue rings. Each separate permutation from the system of generators is constructed on the basis of additions, is characterized by the local action, and leaves fixed the major parts of the components of the element being transformed. A criterion of 2-transitivity of the generated permutation group is given in the form of the strong connectedness of the digraph which corresponds to the system of generators and which is defined on the set of numbers of residue rings in the Cartesian product. Necessary and sufficient conditions under which this group contains an alternating group are formulated.
Originally published in Diskretnaya Matematika (2018) 30, №1, 56–65 (in Russian).
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- On closed classes in partial k-valued logic that contain the class of monotone functions
- On relationship between the parameters characterizing nonlinearity and nonhomomorphy of vector spaces transformation
- Analogues of Gluskin–Hosszú and Malyshev theorems for strongly dependent n-ary operations
- Generation of the alternating group by modular additions
- Formulas for a characteristic of spheres and balls in binary high-dimensional spaces
- Short single tests for circuits with arbitrary stuck-at faults at outputs of gates
- Bounds on the frequencies of tuples on parts of the period of linear recurring sequences over Galois rings
- Compositions of a numerical semigroup
Articles in the same Issue
- Frontmatter
- On closed classes in partial k-valued logic that contain the class of monotone functions
- On relationship between the parameters characterizing nonlinearity and nonhomomorphy of vector spaces transformation
- Analogues of Gluskin–Hosszú and Malyshev theorems for strongly dependent n-ary operations
- Generation of the alternating group by modular additions
- Formulas for a characteristic of spheres and balls in binary high-dimensional spaces
- Short single tests for circuits with arbitrary stuck-at faults at outputs of gates
- Bounds on the frequencies of tuples on parts of the period of linear recurring sequences over Galois rings
- Compositions of a numerical semigroup
