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Title:Some Results on Free Groups in Combinatorial Group Theory
Author(s):Lee, Donghi
Doctoral Committee Chair(s):Sergei v. Ivanov
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract:Let Fm be a free group of a finite rank m ≥ 2. We prove that there exist two elements u 1, u2 ∈ Fm such that every endomorphism y of Fm with non-cyclic image is completely determined by y (u1), y (u2). We obtain this result as a corollary of the construction of a C-test word vn( x1,...,xn), for each n ≥ 2, with the additional property that vn (X1,...,Xn) = 1 if and only if the subgroup ⟨X1,..., Xn⟩ of Fm generated by X1,...,Xn is cyclic. We also prove that every primitivity preserving endomorphism of Fm with m ≥ 3 is an automorphism.
Issue Date:2001
Type:Text
Language:English
Description:67 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001.
URI:http://hdl.handle.net/2142/86777
Other Identifier(s):(MiAaPQ)AAI3017139
Date Available in IDEALS:2015-09-28
Date Deposited:2001


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