Finite index and finite codimension

Shmuel Rosset*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

An old idea of M. Hall on finitely generated subgroups of free groups is developed. We show that it implies that such subgroups have "roots" which are normalizers of certain other subgroups. Similarly in free algebras or group rings of free groups over a field every finitely generated right ideal has a root, which is the unique maximal subalgebra that contains the ideal as an ideal of finite codimension. In analogy to the group case, it is an "idealizer" of another, related, ideal. We also define the "Hall index" of a subgroup of a free group and relate it to Howson's theorem.

Original languageEnglish
Pages (from-to)97-107
Number of pages11
JournalJournal of Pure and Applied Algebra
Volume104
Issue number1
DOIs
StatePublished - 13 Oct 1995

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