Cohen macaulay rings of global dimension two and krull dimension two |
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| Authors: | Yu A Drozd KW Roggenkamp |
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| Institution: | 1. Faculty of Mechanics and Mathematics , Kiev Taras Shevchenko University;2. Math. Institut B , Universit?t Stuttgart |
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| Abstract: | Abstract We construct an example of an IA-automorphism of the free metabelian group of rank n ≥ 3 without nontrivial fixed points. That gives a negative answer to the question raised by Shpilrain in Shpilrain, V. (1998). Fixed points of endomorphisms of a free metabelian group. Math. Proc. Cambridge Philos. Soc. 123(1): 75–83. MR 98k:20056]. By a result of Bachmuth Bachmuth, S. (1965). Automorphisms of free metabelian groups. Trans. Am. Math. Soc. 118:93–1104. MR 31 #4831], such an automorphism does not exist if the rank is equal to 2. |
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| Keywords: | Free metabelian groups IA-automorphisms |
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