The lattice of quasivarieties of commutative moufang loops

1998 ◽  
Vol 37 (6) ◽  
pp. 399-410
Author(s):  
V. I. Ursu
Keyword(s):  
Moufang Loops ◽  
Lattice Of Quasivarieties

An isotopically invariant property of automorphic Moufang loops

2019 ◽  
Vol 58 (4) ◽  
pp. 458-466
Author(s):  
A. N. Grishkov ◽  
M. N. Rasskazova ◽  
L. L. Sabinina
Keyword(s):  
Invariant Property ◽  
Moufang Loops

scholarly journals The restricted Burnside problem for Moufang loops

2021 ◽  
pp. 1-11
Author(s):  
ALEXANDER GRISHKOV ◽  
LIUDMILA SABININA ◽  
EFIM ZELMANOV
Keyword(s):  
Prime Number ◽  
Burnside Problem ◽  
Moufang Loops ◽  
Restricted Burnside Problem ◽  
Positive Integers

Abstract We prove that for positive integers $m \geq 1, n \geq 1$ and a prime number $p \neq 2,3$ there are finitely many finite m-generated Moufang loops of exponent $p^n$ .

scholarly journals Minimally nonassociative nilpotent Moufang loops

2003 ◽  
Vol 268 (1) ◽  
pp. 327-342 ◽  
Author(s):  
Orin Chein ◽  
Edgar G. Goodaire
Keyword(s):  
Moufang Loops

scholarly journals The Moufang loops of order 64 and 81

2007 ◽  
Vol 42 (9) ◽  
pp. 871-883 ◽  
Author(s):  
Gábor P. Nagy ◽  
Petr Vojtěchovský
Keyword(s):  
Moufang Loops

THE MOUFANG LAWS, GLOBAL AND LOCAL

2009 ◽  
Vol 08 (04) ◽  
pp. 477-492 ◽  
Author(s):  
J. D. PHILLIPS
Keyword(s):  
Present Author ◽  
Inverse Property ◽  
Loop Theory ◽  
Traditional Definition ◽  
Moufang Loops ◽  
Definition Of ◽  
Global And Local

There are many possible ways to define Moufang element. We show that the traditional definition is not the most felicitious — for instance, the set of all Moufang elements in an arbitrary loop, qua the traditional definition, need not form a subloop. We offer a new definition of Moufang element that ensures that the set of all Moufang elements in an arbitrary loop is a subloop. Moreover, this definition is "maximally algebraic" with respect to autotopisms. We also give an application of this new definition by showing that a flexible A-element in an inverse property loop is, in fact, a Moufang element, thus sharpening a well-known result of Kinyon, Kunen, and the present author [6]. Finally, we prove that divisible, Moufang groupoids are Moufang loops, thus sharpening a result of Kunen [9], one of the first computer-generated proofs in loop theory.

Commutative Moufang Loops

1971 ◽  
pp. 130-163
Author(s):  
Richard Hubert Bruck
Keyword(s):  
Moufang Loops
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