TY - JOUR
T1 - Malnormal subgroups of free groups
AU - Fine, Benjamin
AU - Myasnikov, Alexei
AU - Rosenberger, Gerhard
PY - 2002/9/1
Y1 - 2002/9/1
N2 - A subgroup H of a group G is malnormal if for any g ∈ G, g ∈ H, then g-1Hg ∩ H = {1}. Here we give a complete characterization of rank 2 malnormal subgroups of free groups. In particular a 2-generator subgroup of a free group F is malnormal if and only if it is isolated and malnormal on generators. The result is not true for greater rank subgroups. This theorem was motivated by a recent algorithm developed by Baumslag, Myasnikov and Remeslennikov that decides whether a subgroup of a free group is malnormal or not.
AB - A subgroup H of a group G is malnormal if for any g ∈ G, g ∈ H, then g-1Hg ∩ H = {1}. Here we give a complete characterization of rank 2 malnormal subgroups of free groups. In particular a 2-generator subgroup of a free group F is malnormal if and only if it is isolated and malnormal on generators. The result is not true for greater rank subgroups. This theorem was motivated by a recent algorithm developed by Baumslag, Myasnikov and Remeslennikov that decides whether a subgroup of a free group is malnormal or not.
UR - http://www.scopus.com/inward/record.url?scp=0036760740&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0036760740&partnerID=8YFLogxK
U2 - 10.1081/AGB-120013310
DO - 10.1081/AGB-120013310
M3 - Article
AN - SCOPUS:0036760740
SN - 0092-7872
VL - 30
SP - 4155
EP - 4164
JO - Communications in Algebra
JF - Communications in Algebra
IS - 9
ER -