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020 _a9783662693650
_9978-3-662-69365-0
024 7 _a10.1007/978-3-662-69365-0
_2doi
050 4 _aQA174-183
072 7 _aPBG
_2bicssc
072 7 _aMAT002010
_2bisacsh
072 7 _aPBG
_2thema
100 1 _aRosebrock, Stephan.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_980109
245 1 0 _aVisual Group Theory
_h[electronic resource] :
_bA Computer-Oriented Geometric Introduction /
_cby Stephan Rosebrock.
250 _a1st ed. 2024.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2024.
300 _aXII, 237 p. 74 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Undergraduate Mathematics Series,
_x2197-4144
505 0 _a1 Introduction to Euclidean Geometry -- 2 Introduction to Groups -- 3 Subgroups and Homomorphisms -- 4 Group Operations -- 5 Group Presentations -- 6 Products of Groups -- 7 Finite Groups -- 8 Abelian and Solvable Groups -- 9 The Hyperbolic Plane -- 10 Hyperbolic Groups.
520 _aThis textbook provides an introduction to group theory starting from the basics, relying on geometry to elucidate its various aspects. Groups naturally manifest as symmetries of geometric shapes, such as reflections and rotations. The book adopts this perspective to provide a straightforward, descriptive explanation, supported by examples and exercises in GAP, an open-source computer algebra system. It covers all of the key concepts of group theory, including homomorphisms, group operations, presentations, products of groups, and finite, abelian, and solvable groups. The topics include cyclic and symmetric groups, dihedral, orthogonal, and hyperbolic groups, as well as the significant notion of Cayley graphs. Self-contained and requiring little beyond high school mathematics, this book is aimed at undergraduate courses and features numerous exercises. It will also appeal to anyone interested in the geometric approach to group theory.
650 0 _aGroup theory.
_970149
650 0 _aGeometry.
_968763
650 0 _aGeometry, Hyperbolic.
_980110
650 1 4 _aGroup Theory and Generalizations.
_970154
650 2 4 _aGeometry.
_968763
650 2 4 _aHyperbolic Geometry.
_980111
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783662693643
776 0 8 _iPrinted edition:
_z9783662693667
830 0 _aSpringer Undergraduate Mathematics Series,
_x2197-4144
_975368
856 4 0 _uhttps://doi.org/10.1007/978-3-662-69365-0
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c61381
_d61381