Profinite group theory, subgroup accessibility, amalgamated products, continuous derivations, Bass-Serre theory

プロ有限群におけるアクセス可能な部分群と、融合積における因子認識について

本稿では、プロ有限群のアクセス可能な部分群が、その完備群環上の自由加群への連続導関数の核として現れることを示し、これを応用して、抽象群の分解をそのプロ有限完備化の分解から導出します。

Profinite Completion of Virtually Free Groups: Recognizing Amalgamated Factors via Continuous Derivations

This paper proves that for a finitely generated virtually free group, a finitely generated subgroup appears as a factor in an amalgamated product decomposition if and only if its closure is a factor in a pro-finite amalgamated product decomposition of the group's profinite completion.