ASUPRA PSEUDOAUTOMORFISMELOR BUCLELOR MEDII BOL

Ion GRECU Moldova State University

Аннотация

A loop is called a middle Bol loop if every loop isotope of satisfies the identity (x ⋅ y)−1 = y−1x−1 (i.e. if the anti-automorphic inverse property is universal in ) [1]. Middle Bol loops are isostrophes of left (right) Bol loops [2, 4]. The left (right, middle) pseudoautomorphisms of middle Bol loops are considered in the present article. The general form of middle Bol loop’s autotopisms is given using right pseudoautomorphisms of the corresponding right Bol loops. Necessary and sufficient conditions when a LP-isotope of a middle Bol loop is isomorphic to are proved. It is shown that in the left (right) Bol loops every middle pseudoautomorphism is a left (right) pseudoautomorphism. Connections between the groups of pseudoautomorphisms (left, right, middle) of a middle Bol loop and of the corresponding left Bol loop are found. Keywords: middle Bol loop, middle (left, right) pseudoautomorphism, autotopy, isostrophy.A loop is called a middle Bol loop if every loop isotope of satisfies the identity (x ⋅ y)−1 = y−1x−1 (i.e. if the anti-automorphic inverse property is universal in ) [1]. Middle Bol loops are isostrophes of left (right) Bol loops [2, 4]. The left (right, middle) pseudoautomorphisms of middle Bol loops are considered in the present article. The general form of middle Bol loop’s autotopisms is given using right pseudoautomorphisms of the corresponding right Bol loops. Necessary and sufficient conditions when a LP-isotope of a middle Bol loop is isomorphic to are proved. It is shown that in the left (right) Bol loops every middle pseudoautomorphism is a left (right) pseudoautomorphism. Connections between the groups of pseudoautomorphisms (left, right, middle) of a middle Bol loop and of the corresponding left Bol loop are found. Keywords: middle Bol loop, middle (left, right) pseudoautomorphism, autotopy, isostrophy.