Colin McLarty writes:
Does anyone here know the origin of the "Whitehead conjecture"? I mean the one saying every group G with Ext(G,Z)=0 is free. Did Whitehead himself consider this, or did it arise by generalizing his ideas? Did he expect it to be true, or just wonder about it?
best, Colin
This isn't definitive, but I think it is approximately correct. The connection between Ext(G,Z)=0 and G being free seems to have first appeared as a reformulation by Henri Cartan of a result of Karl Stein which arose from his work on the "second Cousin problem" in several complex variables. The reference to the paper and review is: @article {MR13:224f, AUTHOR = {Stein, Karl}, TITLE = {Analytische {F}unktionen mehrerer komplexer {V}er\"anderlichen zu vorgegebenen {P}eriodizit\"atsmoduln und das zweite {C}ousinsche {P}roblem}, JOURNAL = {Math. Ann.}, VOLUME = {123}, YEAR = {1951}, PAGES = {201--222}, MRCLASS = {30.0X}, MRNUMBER = {13,224f}, MRREVIEWER = {H. Cartan}, } Whitehead appears to have first posed the question (it doesn't seem to have been a conjecture) at a conference in Warsaw in 1952. The Whitehead problem seems to have been first published by A. Ehrenfeucht in 1955: @article {MR16:994b, AUTHOR = {Ehrenfeucht, A.}, TITLE = {On a problem of {J}. {H}. {C}. {W}hitehead concerning {A}belian groups}, JOURNAL = {Bull. Acad. Polon. Sci. Cl. III.}, VOLUME = {3}, YEAR = {1955}, PAGES = {127--128}, MRCLASS = {20.0X}, MRNUMBER = {16,994b}, MRREVIEWER = {P. A. Smith}, } -- Bob -- Robert L. Knighten Robert@Knighten.org