wilson’s theorem
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2020 ◽  
pp. 1-27
Author(s):  
Aristotelis Panagiotopoulos ◽  
Sławomir Solecki

We represent the universal Menger curve as the topological realization [Formula: see text] of the projective Fraïssé limit [Formula: see text] of the class of all finite connected graphs. We show that [Formula: see text] satisfies combinatorial analogues of the Mayer–Oversteegen–Tymchatyn homogeneity theorem and the Anderson–Wilson projective universality theorem. Our arguments involve only [Formula: see text]-dimensional topology and constructions on finite graphs. Using the topological realization [Formula: see text], we transfer some of these properties to the Menger curve: we prove the approximate projective homogeneity theorem, recover Anderson’s finite homogeneity theorem, and prove a variant of Anderson–Wilson’s theorem. The finite homogeneity theorem is the first instance of an “injective” homogeneity theorem being proved using the projective Fraïssé method. We indicate how our approach to the Menger curve may extend to higher dimensions.



2019 ◽  
Vol 194 ◽  
pp. 1-7
Author(s):  
Alain Connes
Keyword(s):  


2018 ◽  
Vol 49 (5) ◽  
pp. 367-368
Author(s):  
Enrique Treviño
Keyword(s):  








2015 ◽  
Vol 122 (5) ◽  
pp. 433
Author(s):  
Christian Aebi ◽  
Grant Cairns
Keyword(s):  


Author(s):  
Jan Górowski ◽  
Adam Łomnicki

AbstractIn this paper a remarkable simple proof of the Gauss’s generalization of the Wilson’s theorem is given. The proof is based on properties of a subgroup generated by element of order 2 of a finite abelian group. Some conditions equivalent to the cyclicity of (Φ(n), ·n), where n > 2 is an integer are presented, in particular, a condition for the existence of the unique element of order 2 in such a group.



Author(s):  
Daniel Rosenthal ◽  
David Rosenthal ◽  
Peter Rosenthal
Keyword(s):  


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