TY - JOUR
T1 - Finite index subgroups of fully residually free groups
AU - Nikolaev, Andrey V.
AU - Serbin, Denis E.
AU - Kharlampovich, O.
PY - 2011/6
Y1 - 2011/6
N2 - Using graph-theoretic techniques for f.g. subgroups of F[t] we provide a criterion for a f.g. subgroup of a f.g. fully residually free group to be of finite index. Moreover, we show that this criterion can be checked effectively. As an application we obtain an analogue of GreenbergStallings Theorem for f.g. fully residually free groups, and prove that a f.g. nonabelian subgroup of a f.g. fully residually free group is of finite index in its normalizer and commensurator.
AB - Using graph-theoretic techniques for f.g. subgroups of F[t] we provide a criterion for a f.g. subgroup of a f.g. fully residually free group to be of finite index. Moreover, we show that this criterion can be checked effectively. As an application we obtain an analogue of GreenbergStallings Theorem for f.g. fully residually free groups, and prove that a f.g. nonabelian subgroup of a f.g. fully residually free group is of finite index in its normalizer and commensurator.
KW - Fully residually free groups
KW - GreenbergStallings Theorem
KW - finite index
KW - limit groups
UR - http://www.scopus.com/inward/record.url?scp=79959743484&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79959743484&partnerID=8YFLogxK
U2 - 10.1142/S0218196711006388
DO - 10.1142/S0218196711006388
M3 - Article
AN - SCOPUS:79959743484
SN - 0218-1967
VL - 21
SP - 651
EP - 673
JO - International Journal of Algebra and Computation
JF - International Journal of Algebra and Computation
IS - 4
ER -