000			02058nam a22003017a 4500
003			OSt
005			20250728123458.0
008			250728b |||||||| |||| 00| 0 eng d
020			_a9783110372786
020			_a9783111700687 (pbk.) _c€ 49.95
040			_bENG _cIISER-BPR _dIISER-BPR
041			_aENG
082			_a512.4 _bJES _223rd
100			_aJespers, Eric _95470
222			_aMathematics
245			_aGroup ring groups : _bVol. 1 (Orders and generic constructions of units)
250			_a1st Indian ed.
260			_aBerlin: _bWalter de Gruyter GmbH, _c2025.
300			_axii, 447p. : _bill. ; _c24cm.
504			_aIncludes illustrations, references, index of notation and subject index.
520			_aThis two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra. Since the book is addressed to graduate students as well as young researchers, all required background on these diverse areas, both old and new, is included. Supporting problems illustrate the results and complete some of the proofs. Volume 1 contains all the details on describing generic constructions of units and the subgroup they generate. Volume 2 mainly is about structure theorems and geometric methods. Without being encyclopaedic, all main results and techniques used to achieve these results are included. Basic courses in group theory, ring theory and field theory are assumed as background. *Elementary techniques are introduced to built up an intuition for the topic *Gives an overview and structure to a vibrant field of mathematics Author information: Eric Jespers, Vrije Universiteit Brussel, Belgium; Ángel del Río Mateos, Universidad de Murcia, España.
650			_aMathematics
650			_aAlgebra
650			_aRings
650			_aRing groups _95471
700			_aRío, Ángel del _95472
942			_2ddc _cBK
999			_c4263 _d4263