Title: Malnormality and join-free subgroups in right-angled Coxeter groups,
Abstract: In this paper, we prove that all finitely generated malnormal subgroups of
one-ended right-angled Coxeter groups are strongly quasiconvex and they are in
particular quasiconvex when the ambient groups are hyperbolic. The key idea is
to prove all infinite proper malnormal subgroups of one-ended right-angled
Coxeter groups are join-free and then prove the strong quasiconvexity and the
virtual freeness of these subgroups. We also study the subgroup divergence of
join-free subgroups in right-angled Coxeter groups and compare them with the
analogous subgroups in right-angled Artin groups. We characterize almost
malnormal parabolic subgroups in terms of their defining graphs and also
recognize them as strongly quasiconvex subgroups by the recent work of Genevois
and Russell-Spriano-Tran. Finally, we discuss some results on hyperbolically
embedded subgroups in right-angled Coxeter groups.