Let C be a class of finite groups closed under taking subgroups,
quotients, and extensions with abelian kernel. The right-angled Artin
pro-C group GΞβ (pro-C RAAG for short) is the
pro-C completion of the right-angled Artin group G(Ξ)
associated with the finite simplicial graph Ξ.
In the first part, we describe structural properties of pro-C
RAAGs. Among others, we describe the centraliser of an element and show that
pro-C RAAGs satisfy the Tits' alternative, that standard subgroups
are isolated, and that 2-generated pro-p subgroups of pro-C RAAGs
are either free pro-p or free abelian pro-p.
In the second part, we characterise splittings of pro-C RAAGs in
terms of the defining graph. More precisely, we prove that a pro-C
RAAG GΞβ splits as a non-trivial direct product if and only if Ξ
is a join and it splits over an abelian pro-C group if and only if
a connected component of Ξ is a complete graph or it has a complete
disconnecting subgraph. We then use this characterisation to describe an
abelian JSJ decomposition of a pro-C RAAG, in the sense of
Guirardel and Levitt