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Kombinatorische Beweise eines Satzes von Birman und Hilden und eines Satzes von Magnus mit der Theorie der automorphen Mengen und der zugehörigen Zopfgruppenoperationen

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Abstract

We deal with the well-known operation ofARTIN≐S Braid GroupB n on the free groupF n by automorphisms, and give a proof for a theorem ofBIRMAN/HILDEN (here Satz B) by showing, that the images of the generators ofF n underB n are of a special form (Satz C). The theory ofBRIESKORN≐S Automorphic Sets comes in here. With similar methods we give a proof of a theorem of Magnus saying thatB n operates on a certain polynomial ring effectively by automorphisms (here Satz 9.2).

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  1. Bismarckstr. 19, W-5300, Bonn 1, Deutschland

    B. Krüger

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  1. B. Krüger
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Krüger, B. Kombinatorische Beweise eines Satzes von Birman und Hilden und eines Satzes von Magnus mit der Theorie der automorphen Mengen und der zugehörigen Zopfgruppenoperationen. Abh.Math.Semin.Univ.Hambg. 62, 11–27 (1992). https://doi.org/10.1007/BF02941615

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  • DOI: https://doi.org/10.1007/BF02941615

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