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Article: Fixed points of endomorphisms of a free metabelian group
Title  Fixed points of endomorphisms of a free metabelian group 

Authors  
Keywords  Mathematics physics 
Issue Date  1998 
Publisher  Cambridge University Press. 
Citation  Mathematical Proceedings of the Cambridge Philosophical Society, 1998, v. 123 n. 1, p. 7583 How to Cite? 
Abstract  We consider IAendomorphisms (i.e. Identical in Abelianization) of a free metabelian group of finite rank, and give a matrix characterization of their fixed points which is similar to (yet different from) the wellknown characterization of eigenvectors of a linear operator in a vector space. We then use our matrix characterization to elaborate several properties of the fixed point groups of metabelian endomorphisms. In particular, we show that the rank of the fixed point group of an IAendomorphism of the free metabelian group of rank n[gtorequal, slanted]2 can be either equal to 0, 1, or greater than (n−1) (in particular, it can be infinite). We also point out a connection between these properties of metabelian IAendomorphisms and some properties of the Gassner representation of pure braid groups. 
Persistent Identifier  http://hdl.handle.net/10722/53387 
ISSN  2015 Impact Factor: 0.534 2015 SCImago Journal Rankings: 1.069 
DC Field  Value  Language 

dc.contributor.author  Shpilrain, V  en_HK 
dc.date.accessioned  20090403T07:18:25Z   
dc.date.available  20090403T07:18:25Z   
dc.date.issued  1998  en_HK 
dc.identifier.citation  Mathematical Proceedings of the Cambridge Philosophical Society, 1998, v. 123 n. 1, p. 7583  en_HK 
dc.identifier.issn  03050041  en_HK 
dc.identifier.uri  http://hdl.handle.net/10722/53387   
dc.description.abstract  We consider IAendomorphisms (i.e. Identical in Abelianization) of a free metabelian group of finite rank, and give a matrix characterization of their fixed points which is similar to (yet different from) the wellknown characterization of eigenvectors of a linear operator in a vector space. We then use our matrix characterization to elaborate several properties of the fixed point groups of metabelian endomorphisms. In particular, we show that the rank of the fixed point group of an IAendomorphism of the free metabelian group of rank n[gtorequal, slanted]2 can be either equal to 0, 1, or greater than (n−1) (in particular, it can be infinite). We also point out a connection between these properties of metabelian IAendomorphisms and some properties of the Gassner representation of pure braid groups.  en_HK 
dc.language  eng  en_HK 
dc.publisher  Cambridge University Press.  en_HK 
dc.rights  This work is licensed under a Creative Commons AttributionNonCommercialNoDerivatives 4.0 International License.   
dc.rights  Mathematical Proceedings of the Cambridge Philosophical Society. Copyright © Cambridge University Press.  en_HK 
dc.subject  Mathematics physics  en_HK 
dc.title  Fixed points of endomorphisms of a free metabelian group  en_HK 
dc.type  Article  en_HK 
dc.identifier.openurl  http://library.hku.hk:4550/resserv?sid=HKU:IR&issn=03050041&volume=123&issue=1&spage=75&epage=83&date=1998&atitle=Fixed+points+of+endomorphisms+of+a+free+metabelian+group  en_HK 
dc.identifier.email  Shpilrain, V: shpil@submaths.hku.hk  en_HK 
dc.description.nature  published_or_final_version  en_HK 
dc.identifier.hkuros  36438   