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- Title
Intersection problem for Droms RAAGs.
- Authors
Delgado, Jordi; Ventura, Enric; Zakharov, Alexander
- Abstract
We solve the subgroup intersection problem (SIP) for any RAAG G of Droms type (i.e. with defining graph not containing induced squares or paths of length 3): there is an algorithm which, given finite sets of generators for two subgroups H , K ≤ G , decides whether H ∩ K is finitely generated or not, and, in the affirmative case, it computes a set of generators for H ∩ K. Taking advantage of the recursive characterization of Droms groups, the proof consists in separately showing that the solvability of SIP passes through free products, and through direct products with free-abelian groups. We note that most of RAAGs are not Howson, and many (e.g. 𝔽 2 × 𝔽 2 ) even have unsolvable SIP.
- Subjects
SUBGROUP analysis (Experimental design); ARTIN algebras; GRAPHIC methods; ALGORITHMS; GROUP theory
- Publication
International Journal of Algebra & Computation, 2018, Vol 28, Issue 7, p1129
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196718500509