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. 49–72DOI 10.4171/LEM/56-1-2