000			03482nam a22005415i 4500
001			978-1-4614-5450-2
003			DE-He213
005			20140220082820.0
007			cr nn 008mamaa
008			121029s2013 xxu| s |||| 0|eng d
020			_a9781461454502 _9978-1-4614-5450-2
024	7		_a10.1007/978-1-4614-5450-2 _2doi
050		4	_aQA174-183
072		7	_aPBG _2bicssc
072		7	_aMAT002010 _2bisacsh
082	0	4	_a512.2 _223
100	1		_aBencsath, Katalin A. _eauthor.
245	1	0	_aLectures on Finitely Generated Solvable Groups _h[electronic resource] / _cby Katalin A. Bencsath, Marianna C. Bonanome, Margaret H. Dean, Marcos Zyman.
264		1	_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c2013.
300			_aXIV, 52 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aSpringerBriefs in Mathematics, _x2191-8198
505	0		_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.
520			_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.
650		0	_aMathematics.
650		0	_aAlgebra.
650		0	_aGroup theory.
650		0	_aCombinatorics.
650	1	4	_aMathematics.
650	2	4	_aGroup Theory and Generalizations.
650	2	4	_aCombinatorics.
650	2	4	_aAlgebra.
650	2	4	_aGeneral Algebraic Systems.
650	2	4	_aCommutative Rings and Algebras.
700	1		_aBonanome, Marianna C. _eauthor.
700	1		_aDean, Margaret H. _eauthor.
700	1		_aZyman, Marcos. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9781461454496
830		0	_aSpringerBriefs in Mathematics, _x2191-8198
856	4	0	_uhttp://dx.doi.org/10.1007/978-1-4614-5450-2
912			_aZDB-2-SMA
999			_c95412 _d95412