The Burnside ring of finite G-sets

1979 ◽  
pp. 1-13
Author(s):  
Tammo tom Dieck
Keyword(s):  
Burnside Ring

Stable cohomotopy and cobordism of abelian groups

1981 ◽  
Vol 90 (2) ◽  
pp. 273-278 ◽  
Author(s):  
C. T. Stretch
Keyword(s):  
Abelian Group ◽  
Abelian Groups ◽  
Finite Abelian Group ◽  
Formal Group ◽  
Characteristic Class ◽  
Burnside Ring ◽  
Classifying Space ◽  
Formal Group Law ◽  
Stable Cohomotopy ◽  
Group Law

The object of this paper is to prove that for a finite abelian group G the natural map is injective, where Â(G) is the completion of the Burnside ring of G and σ0(BG) is the stable cohomotopy of the classifying space BG of G. The map â is detected by means of an M U* exponential characteristic class for permutation representations constructed in (11). The result is a generalization of a theorem of Laitinen (4) which treats elementary abelian groups using ordinary cohomology. One interesting feature of the present proof is that it makes explicit use of the universality of the formal group law of M U*. It also involves a computation of M U*(BG) in terms of the formal group law. This may be of independent interest. Since writing the paper the author has discovered that M U*(BG) has previously been calculated by Land-weber(5).

scholarly journals A collection of subgroups for the generalized Burnside ring

2009 ◽  
Vol 222 (1) ◽  
pp. 307-317 ◽  
Author(s):  
Fumihito Oda ◽  
Masato Sawabe
Keyword(s):  
Burnside Ring

Irreducible components and isomorphisms of the Burnside ring

2008 ◽  
Vol 11 (6) ◽  
Author(s):  
Wolfgang Kimmerle ◽  
Florian Luca ◽  
Alberto Gerardo Raggi-Cárdenas
Keyword(s):  
Burnside Ring ◽  
Irreducible Components
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