منابع مشابه
The functor of units of Burnside rings for p-groups
In this paper, I describe the structure of the biset functor B sending a p-group P to the group of units of its Burnside ring B(P ). In particular, I show that B is a rational biset functor. It follows that if P is a p-group, the structure of B(P ) can be read from a genetic basis of P : the group B(P ) is an elementary abelian 2-group of rank equal to the number isomorphism classes of rational...
متن کاملBurnside Groups in Knot Theory
Yasutaka Nakanishi asked in 1981 whether a 3-move is an unknotting operation. In Kirby’s problem list, this question is called The Montesinos-Nakanishi 3-move conjecture. We define the nth Burnside group of a link and use the 3rd Burnside group to answer Nakanishi’s question. One of the oldest elementary formulated problems in classical Knot Theory is the 3move conjecture of Nakanishi. A 3-move...
متن کاملSIMPLE p - ADIC GROUPS , II
0.1. For any finite group Γ, a “nonabelian Fourier transform matrix” was introduced in [L1]. This is a square matrix whose rows and columns are indexed by pairs formed by an element of Γ and an irreducible representation of the centralizer of that element (both defined up to conjugation). As shown in [L2], this matrix, which is unitary with square 1, enters (for suitable Γ) in the character for...
متن کاملThe Dixmier Problem, Lamplighters and Burnside Groups
J. Dixmier asked in 1950 whether every non-amenable group admits uniformly bounded representations that cannot be unitarised. We provide such representations upon passing to extensions by abelian groups. This gives a new characterisation of amenability. Furthermore, we deduce that certain Burnside groups are non-unitarisable, answering a question raised by G. Pisier.
متن کاملThe Burnside Ring and Equivariant Cohomotopy for Infinite Groups
After we have given a survey on the Burnside ring of a finite group, we discuss and analyze various extensions of this notion to infinite (discrete) groups. The first three are the finite-G-set-version, the inverselimit-version and the covariant Burnside group. The most sophisticated one is the fourth definition as the equivariant zero-th cohomotopy of the classifying space for proper actions. ...
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: Proceedings of the American Mathematical Society
سال: 1960
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1960-0122870-1