ASUPRA UNOR GRUPURI CONEXE BUCLELOR MEDII BOL

Parascovia SÂRBU, Ion GRECU Department of Fundamental Mathematics, MSU

Rezumat

A loop (Q, ) is called a middle Bol loop if every loop isotope of (Q, ) satisfies the identity 1 1 1 (x y) y x (i.e. if the anti-autmorphic inverse property is universal in (Q, ) ) [6]. The present work continues the investigations from [1] and [5]. Middle Bol loops are isostrophes of left (right) Bol loops [7]. Invariants under this isostrophy are studied and connections between the groups of regular mappings, respectively between the groups of pseudoautomorphisms (left, right, middle), of a middle Bol loop and those of the corresponding right Bol loop are described in this article. A necessary and sufficient condition when the quotient loops of a middle Bol loop and of the corresponding right Bol loop are isomorphic is given. Keywords: Bol loop, middle Bol loop, isostrophes, isostrophy, invariants, universal properties, pseudoautomorphisms.