Statements (17)
| Predicate | Object | 
|---|---|
| gptkbp:instanceOf | 
                                    
                                        
                                            gptkb:mathematical_concept
                                        
                                         | 
                            
| gptkbp:category | 
                                    
                                        
                                            gptkb:algebraic_K-theory
                                        
                                         group theory  | 
                            
| gptkbp:defines | 
                                    
                                        
                                            
                                            The Whitehead group of a group G, denoted Wh(G), is defined as K_1(Z[G])/±G, where K_1 is the first algebraic K-group and Z[G] is the group ring.
                                        
                                        
                                         | 
                            
| gptkbp:field | 
                                    
                                        
                                            gptkb:topology
                                        
                                         | 
                            
| gptkbp:namedAfter | 
                                    
                                        
                                            gptkb:J._H._C._Whitehead
                                        
                                         | 
                            
| gptkbp:notation | 
                                    
                                        
                                            
                                            Wh(G)
                                        
                                        
                                         | 
                            
| gptkbp:property | 
                                    
                                        
                                            
                                            If G is a finite cyclic group, then Wh(G) = 0.
                                        
                                        
                                         If G is a free group, then Wh(G) = 0. If G is a finite abelian group, then Wh(G) is finite.  | 
                            
| gptkbp:relatedTo | 
                                    
                                        
                                            gptkb:algebraic_K-theory
                                        
                                         homotopy theory  | 
                            
| gptkbp:usedIn | 
                                    
                                        
                                            
                                            surgery theory
                                        
                                        
                                         study of h-cobordism theorem  | 
                            
| gptkbp:bfsParent | 
                                    
                                        
                                            gptkb:k-theory
                                        
                                         | 
                            
| gptkbp:bfsLayer | 
                                    
                                        
                                            
                                            5
                                        
                                        
                                         | 
                            
| https://www.w3.org/2000/01/rdf-schema#label | 
                                    
                                        
                                            
                                            Whitehead group
                                        
                                        
                                         |