In group theory, a branch of abstract algebra, the Whitehead problem is the following question:
- Is every abelian group A with Ext1(A, Z) = 0 a free abelian group?
Shelah (1974) proved that Whitehead's problem is undecidable within standard ZFC set theory.
Read more about Whitehead Problem: Refinement, Shelah's Proof, Discussion
Famous quotes containing the words whitehead and/or problem:
“Knowledge shrinks as wisdom grows.”
—Alfred North Whitehead (1861–1947)
“It is part of the educator’s responsibility to see equally to two things: First, that the problem grows out of the conditions of the experience being had in the present, and that it is within the range of the capacity of students; and, secondly, that it is such that it arouses in the learner an active quest for information and for production of new ideas. The new facts and new ideas thus obtained become the ground for further experiences in which new problems are presented.”
—John Dewey (1859–1952)