The finite Bruck loops
نویسندگان
چکیده
منابع مشابه
The Finite Bruck Loops *
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 ...
متن کاملInner mappings of Bruck loops
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 کاملBOL LOOPS AND BRUCK LOOPS OF ORDER pq
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...
متن کاملBruck Loops with Abelian Inner Mapping Groups
Bruck loops with abelian inner mapping groups are centrally nilpotent of class at most 2.
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2011
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2010.11.017