Fiber Spaces and the Eilenberg Homology Groups
George W. Whitehead · Proceedings of the National Academy of Sciences · 1952
products) in the seminormal form, or simply from the standard diagrams themselves, one can construct a matrix A which transforms simultaneously all these elementary matrices according to ( 8).Of course new non-zero elements are introduced which, as yet, it has not seemed possible to keep track of in the general case, but the transformation has been applied to the seminormal form of [3, 2, 1] to yield a representation, which on re- duction modulo 2, 3 or 5 behaves as one would expect.2It seems likely that this direct approach, taken in conjunction with our knowledge of the hook-structure of the diagrams and the ideas outlined above will eventually lead to a complete solution of the problem.