Cyclic complementary extensions and skew-morphism
Year: 2026
Type: article
Abstract: A cyclic complementary extension of a finite group 𝐴 is a finite group 𝐺 which contains 𝐴 and a cyclic subgroup 𝐶 such that A ∩ C = { 1 G } A\cap C=\{1_{G}\} and G = A C G=AC . For any fixed generator 𝑐 of the cyclic factor C = ⟨ c ⟩ C=\langle c\rangle of order 𝑛 in a cyclic complementary extension G = A C G=AC , the equations c x = φ ( x ) c Π ( x ) cx=\varphi(x)c^{\Pi(x)} , x ∈ A x\in A , determine a permutation φ : A → A \varphi\colon A\to A and a function Π : A → Z n \Pi\colon A\to\mathbb{Z}_{n} on 𝐴 characterized by the following properties: φ ( 1 A )
Source: Journal of Group Theory
Authors: Kan Hu, Robert Jajcay
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,712
OpenAlex ID: W7124916528