Prof. F.N. Lion-Cachet

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On the Multiplicative Order of Fn+1/fn modulo Fm

Here, we show that if s �∈ {1, 2, 4} is a fixed positive integer and m and n are coprime positive integers such that the multiplicative order of Fn+1/Fn modulo Fm is s, where Fk is the kth Fibonacci number, then m < 500s2.

Commensurations of Out(Fn)

Let Out(Fn) denote the outer automorphism group of the free group Fn with n > 3. We prove that for any finite index subgroup Γ < Out(Fn), the group Aut(Γ) is isomorphic to the normalizer of Γ in Out(Fn). We prove that Γ is co-Hopfian : every injective homomorphism Γ → Γ is surjective. Finally, we prove that the abstract commensurator Comm(Out(Fn)) is isomorphic to Out(Fn).

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distinct roles in heparan sulfate modifications and embryonic and larval development in Caenorhabditis elegans Katsufumi Dejima , Daisuke Murata, Souhei Mizuguchi, Kazuko H. Nomura, Tomomi Izumikawa, Hiroshi Kitagawa, Keiko Gengyo-Ando , Sawako Yoshina, Tomomi Ichimiya, Shoko Nishihara, Shohei Mitani and Kazuya Nomura* From the Department of Biology, Faculty of Sciences 33, Kyushu University, F...

Prof. Spearman