On joins and intersections of subgroups in free groups
Sergei V. Ivanov
TL;DR
This paper investigates the structure of joins and intersections of finitely generated subgroups in free groups, correcting a previous lemma and providing new insights into their graphical representations.
Contribution
It discredits a prior lemma on subgroup graphs and offers a corrected version, advancing understanding of subgroup interactions in free groups.
Findings
Disproved a lemma of Imrich and Müller.
Provided a corrected version of the lemma.
Enhanced understanding of subgroup graphs in free groups.
Abstract
We study graphs of (generalized) joins and intersections of finitely generated subgroups of a free group. We show how to disprove a lemma of Imrich and M\"uller on these graphs and how to repair this lemma.
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