A Class of Loops Categorically Isomorphic to Bruck Loops of Odd Order
نویسندگان
چکیده
منابع مشابه
A Class of Loops Categorically Isomorphic to Uniquely 2-divisible Bruck Loops
We define a new variety of loops we call Γ-loops. After showing Γ-loops are power associative, our main goal will be showing a categorical isomorphism between uniquely 2-divisible Bruck loops and uniquely 2-divisible Γ-loops. Once this has been established, we can use the well known structure of Bruck loops of odd order to derive the Odd Order, Lagrange and Cauchy Theorems for Γ-loops of odd or...
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Right Bol loops are loops satisfying the identity ((zx)y)x = z((xy)x), and right Bruck loops are right Bol loops satisfying the identity (xy)−1 = x−1y−1. Let p and q be odd primes such that p > q. Advancing the research program of Niederreiter and Robinson from 1981, we classify right Bol loops of order pq. When q does not divide p−1, the only right Bol loop of order pq is the cyclic group of o...
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We continue the work by Aschbacher, Kinyon and Phillips [AKP] as well as of Glauberman [Glaub1,2] by describing the structure of the finite Bruck loops. We show essentially that a finite Bruck loop X is the direct product of a Bruck loop of odd order with either a soluble Bruck loop of 2-power order or a product of loops related to the groups P SL2(q), q = 9 or q ≥ 5 a Fermat prime. The latter ...
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K-loops have their origin in the theory of sharply 2-transitive groups. In this paper a proof is given that K-loops and Bruck loops are the same. For the proof it is necessary to show that in a (left) Bruck loop the left inner mappings L(b)L(a)L(ab)−" are automorphisms. This paper generalizes results of Glauberman[3], Kist[8] and Kreuzer[9].
متن کاملBruck Nets, Codes, and Characters of Loops
Numerous computational examples suggest that if Nk−1 ⊂ Nk are (k− 1)and k-nets of order n, then rankp Nk − rankp Nk−1 ≥ n − k + 1 for any prime p dividing n at most once. We conjecture that this inequality always holds. Using characters of loops, we verify the conjecture in case k = 3, proving in fact that if p ∣∣∣∣n, then rankpN3 ≥ 3n− 2− e, where equality holds if and only if the loop G coörd...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2014
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2013.791304