نتایج جستجو برای: finite moufang loops

تعداد نتایج: 289165  

Journal: :international journal of group theory 2015
karim ahmadidelir

the textit{commutativity degree}, $pr(g)$, of a finite group $g$ (i.e. the probability that two (randomly chosen) elements of $g$ commute with respect to its operation)) has been studied well by many authors. it is well-known that the best upper bound for $pr(g)$ is $frac{5}{8}$ for a finite non--abelian group $g$. in this paper, we will define the same concept for a finite non--abelian textit{...

2007
Gábor P. Nagy

For a loop Q, we call the maps La(x) = ax,Ra(x) = xa left and right translations, respectively. These are permutations of Q, generating the left and right multiplication groups LMlt(Q),RMlt(Q) of Q, respectively. The group closure Mlt(Q) of LMlt(Q) and RMlt(Q) is the full multiplication group of Q. Just like for groups, normal subloops are kernels of homomorphisms of loops. The loop Q is simple...

2002
PETR VOJTĚCHOVSKÝ

Two constructions due to Drápal produce a group by modifying exactly one quarter of the Cayley table of another group. We present these constructions in a compact way, and generalize them to Moufang loops, using loop extensions. Both constructions preserve associators, the associator subloop, and the nucleus. We conjecture that two Moufang 2-loops of finite order n with equivalent associator ca...

2002
ALEŠ DRÁPAL PETR VOJTĚCHOVSKÝ

Certain two constructions, due to Drápal, produce a group by modifying exactly one quarter of the Cayley table of another group. We present these constructions in a compact way, and generalize them to Moufang loops, using loop extensions. Both constructions preserve associators, the associator subloop, and the nucleus. We conjecture that two Moufang 2-loops of finite order n with equivalent ass...

Journal: :Journal of Group Theory 2003

2007
Petr Vojtěchovský PETR VOJTĚCHOVSKÝ

The first class of nonassociative simple Moufang loops was discovered by L. Paige in 1956 [9], who investigated Zorn’s and Albert’s construction of simple alternative rings. M. Liebeck proved in 1987 [7] that there are no other finite nonassociative simple Moufang loops. We can briefly describe the class as follows: For every finite field F, there is exactly one simple Moufang loop. Recall Zorn...

2002
PETR VOJTĚCHOVSKÝ

Moufang loops are one of the best-known generalizations of groups. There is only one countable family of nonassociative finite simple Moufang loops, arising from the split octonion algebras. We prove that every member of this family is generated by three elements, using the classical results on generators of unimodular groups.

Journal: :Mathematical proceedings of the Cambridge Philosophical Society 2021

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

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