Group Invariants of Certain Burn Loop Classes

To any loop (L, ·), one can associate several groups, for example its multiplication groups Gleft(L) and Gright(L) and M(L) = 〈Gleft(L), Gright(L)〉, the groups of (left or right) pseudo-automorphisms, group of automorphisms, or the group of collineations of the associated 3-net. Groups, which are isotope invariants are of special interest. For example, the groups Gleft(L), Gright(L) and M(L) are isotope invariant for any loop L. These groups contain many information about the loop L, the standard references on this field are [2], [4], [11]. For some special loop classes, other isotope invariant groups can be defined. For Bol loops, M. Funk and P.T. Nagy [7] investigated the collineation group generated by the Bol reflections. The notion of the core was first studied by R.H. Bruck [4] for Moufang loops and by V.D. Belousov [3] for Bol loops. Recently, this concept was intensively used in P.T. Nagy and K. Strambach [10]. In the papers [5, 6], R.P. Burn defined the infinite classes B4n, n ≤ 2 and C4n, n ≤ 2, n even of Bol loops. These examples satisfy the left conjugacy closed property, that is, their section