Statements (18)
| 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
|
| https://www.w3.org/2000/01/rdf-schema#label |
Whitehead group
|
| 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
gptkb:k-theory |
| gptkbp:bfsLayer |
5
|