Isotopisms of quadratic quasigroups
Abstract
A quasigroup is a pair ( Q , * ) where Q is a non-empty set and * is a binary operation on Q such that for every ( u , v ) ∈ Q 2 there exists a unique ( x , y ) ∈ Q 2 such that u * x = v = y * u . Let q be an odd prime power, let 𝔽 q denote the finite field of order q , and let ℛ q denote the set of non-zero squares in 𝔽 q . Let ( a , b ) ∈ 𝔽 q 2 be such that { a b , ( a - 1 ) ( b - 1 ) } ⊆ ℛ q . Let 𝒬 a , b denote the quadratic quasigroup ( 𝔽 q , * a , b ) where * a , b is defined by x * a , b y = x + a ( y - x ) if y - x
Fields of Study & Subjects
Mathematics and Applications
Finite Group Theory Research
Advanced Combinatorial Mathematics
Publication details
- Journal / source
- Algebraic Combinatorics
- Volume
- 9
- Issue
- 1
- Pages
- 75–94
- Publication date
- 3 March 2026
- Language
- EN