TY - JOUR
T1 - On endomorphisms of free groups that preserve primitivity
AU - Ivanov, S. V.
N1 - Funding Information:
*) Supported in part by an Alfred P. Sloan Research Fellowship, a Beckman Fellowship, and NSF Grant DMS 95-01056.
PY - 1999/2/3
Y1 - 1999/2/3
N2 - It is proven that if φ is an endomorphism of a free group Fn = 1, ⋯, Xn> of rank n such that φ(u) is primitive whenever so is u ∈ Fn and φ(Fn) contains a primitive pair (i.e., a pair α(x1), α(x2) with α ∈ Aut fn), then φ is an automorphism. Also, every endomorphism of F2 that preserves primitivity is an automorphism.
AB - It is proven that if φ is an endomorphism of a free group Fn = 1, ⋯, Xn> of rank n such that φ(u) is primitive whenever so is u ∈ Fn and φ(Fn) contains a primitive pair (i.e., a pair α(x1), α(x2) with α ∈ Aut fn), then φ is an automorphism. Also, every endomorphism of F2 that preserves primitivity is an automorphism.
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U2 - 10.1007/s000130050309
DO - 10.1007/s000130050309
M3 - Article
AN - SCOPUS:0033248811
SN - 0003-889X
VL - 72
SP - 92
EP - 100
JO - Archiv der Mathematik
JF - Archiv der Mathematik
IS - 2
ER -