JournalslemVol. 56, No. 1/2pp. 49–72

A Wreath Product Approach to Classical Subgroup Theorems

  • Luis Ribes

    Carleton University, Ottawa, Canada

  • Benjamin Steinberg

    City College of New York, USA
A Wreath Product Approach to Classical Subgroup Theorems cover
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Abstract

We provide elementary proofs of the Nielsen-Schreier Theorem and the Kurosh Subgroup Theorem via wreath products. Our proofs are diagrammatic in nature and work simultaneously in the abstract and profinite categories. A new proof that open subgroups of quasifree profinite groups are quasifree is also given.

Cite this article

Luis Ribes, Benjamin Steinberg, A Wreath Product Approach to Classical Subgroup Theorems. Enseign. Math. 56 (2010), no. 1/2, pp. 49–72

DOI 10.4171/LEM/56-1-2