Results 11 to 20 of about 404 (37)

Exceptional smooth Bol loops

International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 9, Page 575-579, 2002., 2002
One new class of smooth Bol loops, exceptional Bol loops, is introduced and studied. The approach to the Campbell‐Hausdorff formula is outlined. Bol‐Bruck loops and Moufang loops are exceptional which justifies our consideration.
Larissa V. Sbitneva
wiley   +1 more source

Loops embedded in generalized Cayley algebras of dimension 2r, r ≥ 2

International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 3, Page 181-187, 2001., 2001
Every Cayley algebra of dimension 2r, r ≥ 2, contains an embedded invertible loop of order 2r+1 generated by its basis. Such a loop belongs to a class of non‐abelian invertible loops that are flexible and power‐associative.
Raoul E. Cawagas
wiley   +1 more source

Infinite Simple Bol Loops [PDF]

, 2004
If the left multiplication group of a loop is simple, then the loop is simple. We use this observation to give examples of infinite simple Bol loops.Comment: 4 pages, AMS-LaTeX, to appear in Comment. Math. Univ.
Kiechle, Hubert, Kinyon, Michael K.
core   +1 more source

Non-associative geometry and discrete structure of spacetime [PDF]

, 2000
A new mathematical theory, non-associative geometry, providing a unified algebraic description of continuous and discrete spacetime, is introduced.Comment: LATeX2e file, 11 pages, talk given at "Loop's 99 meeting" (Prague, July 27 - August 1, 1999). To
Nesterov, Alexander I., Sabinin, Lev. V.
core   +1 more source

n-Ary quasigroups of order 4

, 2008
We characterize the set of all N-ary quasigroups of order 4: every N-ary quasigroup of order 4 is permutably reducible or semilinear. Permutable reducibility means that an N-ary quasigroup can be represented as a composition of K-ary and (N-K+1)-ary ...
Denis S. Krotov, Krotov D. S., Vladimir N. Potapov   +2 more
core   +1 more source

Cheban loops

, 2010
Left Cheban loops are loops that satisfy the identity x(xy.z) = yx.xz. Right Cheban loops satisfy the mirror identity {(z.yx)x = zx.xy}. Loops that are both left and right Cheban are called Cheban loops.
Phillips, J. D., Shcherbacov, V. A.
core   +1 more source

The smallest Moufang loop revisited [PDF]

, 2007
We derive presentations for Moufang loops of type $M(G,2)$, defined by Chein, with $G$ finite, two-generated.
Vojtěchovský, Petr
core  

Gyrogroups associated with groups

Communications in Algebra, 2022
Vipul Kakkar
exaly  

Moufang Loops that Share Associator and Three Quarters of Their Multiplication Tables

Rocky Mountain Journal of Mathematics, 2006
Ales Drapal, Petr Vojtěchovský
exaly  

On Twisted Subgroups and Bol Loops of Odd Order

Rocky Mountain Journal of Mathematics, 2006
Michael K Kinyon
exaly