论文信息 - Diassociativity in Conjugacy Closed Loops

Diassociativity in Conjugacy Closed Loops

Abstract Let Q be a conjugacy closed loop, and N(Q) its nucleus. Then Z(N(Q)) contains all associators of elements of Q. If in addition Q is diassociative (i.e., an extra loop), then all these associators have order 2. If Q is power-associative and |Q| is finite and relatively prime to 6, then Q is a group. If Q is a finite non-associative extra loop, then 16 ∣ |Q|.

[1] James Osborn,et al. Loops with the weak inverse property. , 1960 .

[2] E. G. Goodaire,et al. A Class of Loops Which are Isomorphic to all Loop Isotopes , 1982, Canadian Journal of Mathematics.

[3] E. G. Goodaire,et al. Some Special Conjugacy Closed Loops , 1990, Canadian Mathematical Bulletin.

[4] R. H. Bruck,et al. Loops Whose Inner Mappings are Automorphisms , 1956 .

[5] Loops and the Lagrange Property , 2002, math/0205141.

[6] E. G. Goodaire,et al. SEMI-DIRECT PRODUCTS AND BOL LOOP , 1994 .

[7] William McCune,et al. OTTER 3.0 Reference Manual and Guide , 1994 .

[8] Hantao Zhang,et al. SEM: a System for Enumerating Models , 1995, IJCAI.

[9] K. Kunen. The structure of conjugacy closed loops , 2000 .

[10] R. H. Bruck. A Survey of Binary Systems , 1971 .

[11] R. H. Bruck. Contributions to the theory of loops , 1946 .

[12] H. O. Pflugfelder. Quasigroups and loops : introduction , 1990 .