000 | 03604nam a22005777a 4500 | ||
---|---|---|---|
001 | sulb-eb0022281 | ||
003 | BD-SySUS | ||
005 | 20160413122241.0 | ||
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 | _aCommutative algebra. | |
650 | 0 | _aCommutative rings. | |
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 | ||
942 |
_2Dewey Decimal Classification _ceBooks |
||
999 |
_c44373 _d44373 |