Symmetric Groups as Products of Abelian Subgroups |
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| Authors: | Abert Miklos |
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| Institution: | Department of Algebra and Number Theory, Eötvös University Kecskeméti utca 10–12, H-1053 Budapest, Hungary; abert{at}math-inst.hu |
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| Abstract: | A proof is given that the full symmetric group over any infiniteset is the product of finitely many Abelian subgroups. In fact,289 subgroups suffice. Sharp bounds are also obtained on theminimal number k, such that the finite symmetric group Sn isthe product of k Abelian subgroups. Using this, Sn is provedto be the product of 72n1/2(log n)3/2 cyclic subgroups. 2000Mathematics Subject Classification 20B30, 20D40. |
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