Free groups may be viewed as the fundamental groups of graphs. This observation allows for a very intuitive view of free groups and their subgroups. These lectures combine topological ideas, due to Stallings in the 1980s, with more combinatorial and computational ones to prove many of the fundamental results in free groups. These results include the Nielsen-Schreier Theorem (subgroups of free groups are free), Howson's Theorem (finitely generated subgroups have finitely generated intersection), and the decidability of the subgroup membership problem.
Playlist - Free groups via graphs
Free groups may be viewed as the fundamental groups of graphs. This observation allows for a very intuitive view of free groups and their subgroups. These lectures combine topological ideas, due to Stallings in the 1980s, with more combinatorial and computational ones to prove many of the fundamental results in free groups. These results include the Nielsen-Schreier Theorem (subgroups of free groups are free), Howson's Theorem (finitely generated subgroups have finitely generated intersection), and the decidability of the subgroup membership problem.
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