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Intersection problem for Droms RAAGs

Preprint

<p>We solve the subgroup intersection problem (SIP) for any RAAG G of Droms type<br /> (i.e., with defining graph not containing induced squares or paths of length 3): there is<br /> an algorithm which, given finite sets of generators for two subgroups H,K of\&nbsp;G, decides<br /> whether H \cap K is finitely generated or not, and, in the affirmative case, it computes<br /> a set of generators for H \cap K. Taking advantage of the recursive characterization of<br /> Droms groups, the proof consists in separately showing that the solvability of SIP passes<br /> through free products, and through direct products with free-abelian groups. We note<br /> that most of RAAGs are not Howson, and many (e.g. F2 x F2) even have unsolvable SIP.</p>

Jordi Delgado

Enric Ventura

Alexander Zakharov

Publication

Year of publication: 2017

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