Cyclic m-DCI-groups and m-CI-groups
Year: 2025
Type: article
Abstract: Based on the earlier work of Li from 1997 and Dobson from 2008, in this paper we complete the classification of cyclic m-DCI-groups and m-CI-groups. For a positive integer m such that m ≥ 3, we show that the group ℤ_(n) is an m-DCI-group if and only if n is not divisible by 8 nor by p² for any odd prime p < m. Furthermore, if m ≥ 6, then we show that ℤn is an m-CI-group if and only if either n ∈ {8, 9, 18}, or n ∉ {8, 9, 18} and n is not divisible by 8 nor by p² for any odd prime p < (m - 1)/2.
Authors: Istvan Kovács, Luka Šinkovec
Institution: University of Primorska
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Awards: Symmetries in graphs via rigid cells, Terwilliger algebra of a graph, Geometries, Graphs, Groups and their Links, Automorphisms and Isomorphisms of Finite Graphs, Hamilton cycles with rotational symmetry in connected vertex-transitive graphs, Algebra, discrete mathematics, probability and game theory
OpenAlex ID: W4407876094