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On the Magnus–Smelkin embedding

Published online by Cambridge University Press:  20 January 2009

J. Mccool∗
J. Mccool∗
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Canada M5S 1A1
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The generalization of the Magnus embedding [7] proved by Smelkin [9] may bestated as follows. Let L be a free group freely generated by the set xi(i∈I), and let R be a normal subgroup of L with G = L/R. If V is any variety of groups and ∏ is the V-freegroup with free generating set the symbols [g, xi] (g∈G, i∈I), then L/V(R) is embeddedin the semidirect product ∏ ⋊ G (where the action of G on ∏ is given by h · [g, xi] = [hg, xi], for h, g ∈ G).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 30 , Issue 1 , February 1987 , pp. 133 - 142
Copyright
Copyright © Edinburgh Mathematical Society 1987

References

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