LEADER 04666nam 22007815 450 001 9910438148503321 005 20220415200421.0 010 $a1-283-90905-7 010 $a1-4614-5450-6 024 7 $a10.1007/978-1-4614-5450-2 035 $a(CKB)2670000000278243 035 $a(EBL)1081924 035 $a(OCoLC)818827923 035 $a(SSID)ssj0000799759 035 $a(PQKBManifestationID)11497649 035 $a(PQKBTitleCode)TC0000799759 035 $a(PQKBWorkID)10765056 035 $a(PQKB)10348419 035 $a(DE-He213)978-1-4614-5450-2 035 $a(MiAaPQ)EBC1081924 035 $a(PPN)16830306X 035 $a(EXLCZ)992670000000278243 100 $a20121029d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLectures on finitely generated solvable groups$b[electronic resource] /$fby Katalin A. Bencsath, Marianna C. Bonanome, Margaret H. Dean, Marcos Zyman 205 $a1st ed. 2013. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d2013. 215 $a1 online resource (62 p.) 225 1 $aSpringerBriefs in Mathematics,$x2191-8198 300 $aDescription based upon print version of record. 311 $a1-4614-5449-2 320 $aIncludes bibliographical references. 327 $aForeword -- Preface.-  Preliminaries.-  Tools: Presentations and their Calculus.-  Constructions -- Representations and a Theorem of Krasner and Kaloujnine.- The Bieri-Strebel Theorems -- Finitely Generated Metabelian Groups -- An Embedding Theorem for Finitely Generated Metabelian Groups .- Sketch of Proof of Lemma 1.1 -- Theorem 2.1 Details -- Presenting an (Internal) HNN-Extension -- References. 330 $aLectures on Finitely Generated Solvable Groups are based on the ?Topics in Group Theory" course focused on finitely generated solvable groups that was given by Gilbert G. Baumslag at the Graduate School and University Center of the City University of New York.  While knowledge about finitely generated nilpotent groups is extensive, much less is known about the more general class of solvable groups containing them.  The study of finitely generated solvable groups involves many different threads; therefore these notes contain discussions on HNN extensions; amalgamated and wreath products; and other concepts from combinatorial group theory as well as commutative algebra.  Along with Baumslag?s Embedding Theorem for Finitely Generated Metabelian Groups, two theorems of Bieri and Strebel are presented to provide a solid foundation for understanding the fascinating class of finitely generated solvable groups.  Examples are also supplied, which help illuminate many of the key concepts contained in the notes.  Requiring only a modest initial group theory background from graduate and post-graduate students, these notes provide a field guide to the class of finitely generated solvable groups from a combinatorial group theory perspective. 410 0$aSpringerBriefs in Mathematics,$x2191-8198 606 $aGroup theory 606 $aCombinatorics 606 $aAlgebra 606 $aCommutative algebra 606 $aCommutative rings 606 $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078 606 $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 606 $aGeneral Algebraic Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/M1106X 606 $aCommutative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11043 615 0$aGroup theory. 615 0$aCombinatorics. 615 0$aAlgebra. 615 0$aCommutative algebra. 615 0$aCommutative rings. 615 14$aGroup Theory and Generalizations. 615 24$aCombinatorics. 615 24$aAlgebra. 615 24$aGeneral Algebraic Systems. 615 24$aCommutative Rings and Algebras. 676 $a515.7242 700 $aBencsath$b Katalin A$4aut$4http://id.loc.gov/vocabulary/relators/aut$01061366 702 $aBonanome$b Marianna C$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aDean$b Margaret H$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aZyman$b Marcos$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910438148503321 996 $aLectures on Finitely Generated Solvable Groups$92518593 997 $aUNINA