اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدCode loops in dimension at most 8
37
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Code loops are certain Moufang $2$-loops constructed from doubly even binary codes that play an important role in the construction of local subgroups of sporadic groups. More precisely, code loops are central extensions of the group of order $2$ by an elementary abelian $2$-group $V$ in the variety of loops such that their squaring map, commutator map and associator map are related by combinatorial polarization and the associator map is a trilinear alternating form. Using existing classifications of trilinear alternating forms over the field of $2$ elements, we enumerate code loops of dimension $d=mathrm{dim}(V)le 8$ (equivalently, of order $2^{d+1}le 512$) up to isomorphism. There are $767$ code loops of order $128$, and $80826$ of order $256$, and $937791557$ of order $512$.
قيم البحث
اقرأ أيضاً
Let $N(n)$ denote the number of isomorphism types of groups of order $n$. We consider the integers $n$ that are products of at most $4$ not necessarily distinct primes and exhibit formulas for $N(n)$ for such $n$.
The groups whose orders factorise into at most four primes have been described (up to isomorphism) in various papers. Given such an order n, this paper exhibits a new explicit and compact determination of the isomorphism types of the groups of order
n together with effective algorithms to enumerate, construct, and identify these groups. The algorithms are implemented for the computer algebra system GAP.
$D$-loops are loops with the antiautomorphic inverse property. The class of such loops is larger than the class of IP-loops. The smallest $D$-loops which is not an IP-loop has six elements. We prove several basic properties of such loops and present
methods of constructions of $D$-loops from IP-loops. Unfortunately, a loop isotopic to a $D$-loop may not be a $D$-loop.
A theorem by Hall asserts that the multiplication in torsion free nilpotent groups of finite Hirsch length can be facilitated by polynomials. In this note we exhibit explicit Hall polynomials for the torsion free nilpotent groups of Hirsch length at most 5.
The purpose of these old notes (written in 1998 during a research project on holonomy of pseudo-Riemannian manifolds of type (10,1)) is to determine the orbit structure of the groups Spin(p,q) acting on their spinor spaces for the values (p,q) = (8,0
), (9,0), (9,1), (10,0), (10,1), and (10,2). Im making them available on the arXiv because I continue to get requests for them as well as questions about how they can be cited.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
