Classes of piecewise-quasiaffine transformations on the generalized 2-group of quaternions
-
Boris A. Pogorelov
and
Marina A. Pudovkina
Abstract
The class of nonabelian 2-groups H with cyclic subgroup of index 2 includes the dihedral group, the generalized quaternion group, the semidihedral group, and the modular maximal cyclic group, which have many various applications in discrete mathematics and cryptography. We introduce piecewise-quasiaffine transformations on a group H, and put forward criteria of their bijectivity. For the generalized group of quaternions of order 2m, we obtain a complete classification of orthomorphisms, complete transformations, and their left analogues in the class of piecewise-quasiaffine transformations under consideration. We also evaluate their cardinalities.
Originally published in Diskretnaya Matematika (2022) 34, №1, 23–35 (in Russian).
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Articles in the same Issue
- Frontmatter
- On small distance-regular graphs with the intersection arrays {mn − 1, (m − 1)(n + 1), n − m + 1; 1, 1, (m − 1)(n + 1)}
- On algebraicity of lattices of ω-fibred formations of finite groups
- On polynomial-modular recursive sequences
- Classes of piecewise-quasiaffine transformations on the generalized 2-group of quaternions
- Limit theorem for a smoothed version of the spectral test for testing the equiprobability of a binary sequence
- Limit theorem for stationary distribution of a critical controlled branching process with immigration
Articles in the same Issue
- Frontmatter
- On small distance-regular graphs with the intersection arrays {mn − 1, (m − 1)(n + 1), n − m + 1; 1, 1, (m − 1)(n + 1)}
- On algebraicity of lattices of ω-fibred formations of finite groups
- On polynomial-modular recursive sequences
- Classes of piecewise-quasiaffine transformations on the generalized 2-group of quaternions
- Limit theorem for a smoothed version of the spectral test for testing the equiprobability of a binary sequence
- Limit theorem for stationary distribution of a critical controlled branching process with immigration
