On the Burnside ring and stable cohomotopy of a finite group.
نویسندگان
چکیده
منابع مشابه
The Burnside Ring and Equivariant Stable 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 zero-th equivariant stable cohomotopy of the classifying space for proper ac...
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. ...
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This paper introduces two new Burnside rings for a finite group G, called the slice Burnside ring and the section Burnside ring. They are built as Grothendieck rings of the category of morphisms of G-sets, and of Galois morphisms of G-sets, respectively. The well known results on the usual Burnside ring, concerning ghost maps, primitive idempotents, and description of the prime spectrum, are ex...
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In this note we present an algorithm for the construction of the unit group of the Burnside ring Ω(G) of a finite group G from a list of representatives of the conjugacy classes of subgroups of G.
متن کاملA Note on the Λ-structure on the Burnside Ring
Let G be a finite group and let S be a G-set. The Burnside ring of G has a natural structure of a λ-ring, {λn}n∈N. However, a priori λ (S) can only be computed recursively, by first computing λ(S), . . . , λ(S). In this paper we establish an explicit formula, expressing λ(S) as a linear combination of classes of G-sets.
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1979
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-11795