TY - JOUR
TI - Finiteness results for subgroups of finite extensions
AU - Araújo, V.
AU - Silva, P.V.
AU - Sykiotis, M.
JO - Journal of Algebraic Combinatorics
PY - 2015
VL - 423
TODO - null
SP - 592-614
PB - Academic Press Inc.
SN - 0925-9899
TODO - 10.1016/j.jalgebra.2014.10.033
TODO - null
TODO - We discuss in the context of finite extensions two classical theorems of Takahasi and Howson on subgroups of free groups. We provide bounds for the rank of the intersection of subgroups within classes of groups such as virtually free groups, virtually nilpotent groups or fundamental groups of finite graphs of groups with virtually polycyclic vertex groups and finite edge groups. As an application of our generalization of Takahasi's Theorem, we provide a uniform bound for the rank of the periodic subgroup of any endomorphism of the fundamental group of a given finite graph of groups with finitely generated virtually nilpotent vertex groups and finite edge groups. © 2014 Elsevier Inc.
ER -