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1、CommunicationsinAlgebraISSN:0092-7872(Print)1532-4125(Online)Journalhomepage:http://www.tandfonline.com/loi/lagb20CyclicnormalsubgroupsofgeneralizedBaumslag–SolitargroupsAlbertoL.Delgado,DerekJ.S.Robinson&MathewTimmTocitethisarticle:AlbertoL.Delgado,DerekJ.S.Robinso
2、n&MathewTimm(2017)CyclicnormalsubgroupsofgeneralizedBaumslag–Solitargroups,CommunicationsinAlgebra,45:4,1808-1818,DOI:10.1080/00927872.2016.1226859Tolinktothisarticle:http://dx.doi.org/10.1080/00927872.2016.1226859Acceptedauthorversionpostedonline:07Oct2016.Publishe
3、donline:07Oct2016.SubmityourarticletothisjournalArticleviews:22ViewrelatedarticlesViewCrossmarkdataFullTerms&Conditionsofaccessandusecanbefoundathttp://www.tandfonline.com/action/journalInformation?journalCode=lagb20Downloadby:[SeoulNationalUniversity]Date:07Decembe
4、r2016,At:02:15COMMUNICATIONSINALGEBRA®2017,VOL.45,NO.4,1808–1818http://dx.doi.org/10.1080/00927872.2016.1226859CyclicnormalsubgroupsofgeneralizedBaumslag–SolitargroupsabcAlbertoL.Delgado,DerekJ.S.Robinson,andMathewTimmaDepartmentofMathematics,IllinoisStateUniversity
5、,Normal,Illinois,USA;bDepartmentofMathematics,UniversityofIllinoisatUrbana-Champaign,Urbana,Illinois,USA;cDepartmentofMathematics,BradleyUniversity,Peoria,Illinois,USAABSTRACTARTICLEHISTORYThecentersandcyclicradicalsofgeneralizedBaumslag–SolitargroupsReceived25Febru
6、ary2015(GBS-groups)arestudied.Criteriafortheirnon-trivialityarefoundandanRevised16February2016algorithmtocomputethecenterandcyclicradicalisgiven.Inaddition,foreachCommunicatedbyunimodularGBS-group,aGBS-cover,i.e.,aGBS-groupinwhoseunderlyingS.Hermillergraphtheweights
7、aroundeachvertexareconstantinabsolutevalue,isKEYWORDSconstructed.Thesegroupsarethencharacterizedbyaminimalityproperty.Coveringgroup;cyclicradical;generalizedBaumslag–Solitargroup2010MATHEMATICSSUBJECTCLASSIFICATIONPrimary:20E061.IntroductionAgeneralizedBaumslag–Soli
8、targroup,orGBS-group,isthefundamentalgroupofagraphofgroupswithinnitecyclicvertexandedgegroups.GBS-groupshavebeenthesubjectofnumerousrecen
