Article collection "Mathematical Problems of Cybernetics" №2, Moscow, 1989
Authors:Marchenkov S.S.
The classification of algebras with alternating automorphism group
Abstract:
We study algebras бE; Fс with a finite support E, containing no less than four elements and having an
alternating automorphism group. The algebras бE; Fс, бE; Gс are said to be equivalent if the clones generated by the sets of operations F and G coincide. We prove that up to equivalence for |E|=4 the number of such algebras is exactly 20 and for |E|>4 the number is 8|E| — 11.
Keywords:
classification of finite algebras, alternating automorphism group