The Nielsen-Schreier Theorem states that every subgroup of a free group is itself a free group. Proved by Jakob Nielsen and Otto Schreier, it is a foundational result of combinatorial group theory, and it has a well known proof via covering spaces of graphs that links the algebraic statement directly to topology.
Facts
StatementThe Nielsen-Schreier theorem states that every subgroup of a free group is itself free. 1 Proof YearJakob Nielsen proved a restricted finitely-generated case in 1921; Otto Schreier proved the theorem in full generality in his 1926 habilitation thesis, published 1927. Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
In Branch
Proved By
Source Nielsen-Schreier Theorem (Wikipedia)
Sources
1. Nielsen-Schreier Theorem (Wikipedia)
Wikimedia FoundationLead paragraph, first sentence
In group theory, a branch of mathematics, the Nielsen-Schreier theorem states that every subgroup of a free group is itself free.
History section, Schreier sentence
Otto Schreier proved the Nielsen-Schreier theorem in its full generality in his 1926 habilitation thesis, Die Untergruppen der freien Gruppe, also published in 1927 in Abh. math. Sem. Hamburg. Univ.
In Group: Group Theory, Lead section
In group theory, a branch of mathematics, the Nielsen-Schreier
Proved By: Otto Schreier, Lead
It is named after Jakob Nielsen and Otto Schreier.
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