Homotopy groups, commutators, and $\Gamma$-groups
نویسندگان
چکیده
منابع مشابه
On local gamma factors for orthogonal groups and unitary groups
In this paper, we find a relation between the proportionality factors which arise from the functional equations of two families of local Rankin-Selberg convolutions for irreducible admissible representations of orthogonal groups, or unitary groups. One family is that of local integrals of the doubling method, and the other family is that of local integrals expressed in terms of sph...
متن کاملOn Commutators in Groups
Commutators originated over 100 years ago as a by-product of computing group characters of nonabelian groups. They are now an established and immensely useful tool in all of group theory. Commutators became objects of interest in their own right soon after their introduction. In particular, the phenomenon that the set of commutators does not necessarily form a subgroup has been well documented ...
متن کاملOn braid groups and homotopy groups
The purpose of this article is to give an exposition of certain connections between the braid groups [1, 3] and classical homotopy groups which arises in joint work of Jon Berrick, Yan-Loi Wong and the authors [8, 2, 32]. These connections emerge through several other natural contexts such as Lie algebras attached to the descending central series of pure braid groups arising as Vassiliev invari...
متن کاملArtin Braid Groups and Homotopy Groups
We study the Brunnian subgroups and the boundary Brunnian subgroups of the Artin braid groups. The general higher homotopy groups of the sphere are given by mirror symmetric elements in the quotient groups of the Artin braid groups modulo the boundary Brunnian braids, as well as given as a summand of the center of the quotient groups of Artin pure braid groups modulo boundary Brunnian braids. T...
متن کاملON COMMUTATORS IN p-GROUPS
For a given prime p, what is the smallest integer n such that there exists a group of order p in which the set of commutators does not form a subgroup? In this paper we show that n = 6 for any odd prime and n = 7 for p = 2.
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: Illinois Journal of Mathematics
سال: 1960
ISSN: 0019-2082
DOI: 10.1215/ijm/1255455732