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- Title
Note on a theorem of Magnus.
- Authors
Blackburn, Norman
- Abstract
Magnus [4] proved the following theorem. Suppose that F is free group and that X is a basis of F. Let R be a normal subgroup of F and write G = F/R. Then there is a monomorphism of F/R′ in which ; here the tx are independent parameters permutable with all elements of G. Later investigations [1, 3] have shown what elements can appear in the south-west corner of these 2 × 2 matrices. In this form the theorem subsequently reappeared in proofs of the cup-product reduction theorem of Eilenberg and MacLane (cf. [7, 8]). In this note a direct group-theoretical proof of the theorems will be given.
- Publication
Journal of the Australian Mathematical Society, 1969, Vol 10, Issue 3/4, p469
- ISSN
1446-7887
- Publication type
Article
- DOI
10.1017/S1446788700007734