Classes of piecewise quasiaffine transformations on dihedral, quasidihedral and modular maximal-cyclic 2-groups
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Boris A. Pogorelov
and
Marina A. Pudovkina
Abstract
Nonabelian 2-groups H containing a cyclic subgroup of index 2 are dihedral groups, generalized quaternion groups, quasidihedral groups and modular maximal-cyclic groups. Earlier the authors introduced the classes of piecewise quasiaffine transformations on an arbitrary nonabelian 2-group H with a cyclic subgroup of index 2. For the generalized group of quaternions of order 2m we have obtained a complete classification of orthomorphisms, complete transformations and their left analogues in the class of piecewise quasiaffine transformations under consideration. This paper presents a similar classification for the remaining three groups (the dihedral group, the quasidihedral group and the modular maximal-cyclic group).
Originally published in Diskretnaya Matematika (2022) 34, №2, 50–66 (in Russian).
References
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Articles in the same Issue
- Frontmatter
- Weakly supercritical branching process in unfavourable environment
- Classes of piecewise quasiaffine transformations on dihedral, quasidihedral and modular maximal-cyclic 2-groups
- On the multiplicative complexity of polynomials
- On the complexity of realizations of Boolean functions in some classes of hypercontact circuits
- On the rate of convergence of quasigroup convolutions of probability distributions
Articles in the same Issue
- Frontmatter
- Weakly supercritical branching process in unfavourable environment
- Classes of piecewise quasiaffine transformations on dihedral, quasidihedral and modular maximal-cyclic 2-groups
- On the multiplicative complexity of polynomials
- On the complexity of realizations of Boolean functions in some classes of hypercontact circuits
- On the rate of convergence of quasigroup convolutions of probability distributions
