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Sergei v. Ivanov Lee, Donghi 2015-09-28T15:19:29Z 2015-09-28T15:19:29Z 10000-01-01 2001 2001 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. Made available in DSpace on 2015-09-28T15:19:29Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3017139.pdf: 2719348 bytes, checksum: a2785a0933fd3c99f1fd7d1aa657cd19 (MD5) Previous issue date: 2001 Embargo set by: Seth Robbins for item 88058 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 67 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001. http://hdl.handle.net/2142/86777 (MiAaPQ)AAI3017139 eng Mathematics Some Results on Free Groups in Combinatorial Group Theory text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.