000			03332nam a22004935i 4500
001			978-1-4757-4034-9
003			DE-He213
005			20210118114613.0
007			cr nn 008mamaa
008			130128s1988 xxu| s |||| 0|eng d
020			_a9781475740349 _9978-1-4757-4034-9
024			_a10.1007/978-1-4757-4034-9 _2doi
050			_aQA174-183
072			_aPBG _2bicssc
072			_aMAT002010 _2bisacsh
072			_aPBG _2thema
082			_a512.2 _223
100			_aArmstrong, Mark A. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut
245			_aGroups and Symmetry _h[electronic resource] / _cby Mark A. Armstrong.
250			_a1st ed. 1988.
264			_aNew York, NY : _bSpringer New York : _bImprint: Springer, _c1988.
300			_aXI, 187 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490			_aUndergraduate Texts in Mathematics, _x0172-6056
505			_a1 Symmetries of the Tetrahedron -- 2 Axioms -- 3 Numbers -- 4 Dihedral Groups -- 5 Subgroups and Generators -- 6 Permutations -- 7 Isomorphisms -- 8 Plato’s Solids and Cayley’s Theorem -- 10 Products -- 11 Lagrange’s Theorem -- 12 Partitions -- 13 Cauchy’s Theorem -- 14 Conjugacy -- 15 Quotient Groups -- 16 Homomorphisms -- 17 Actions, Orbits, and Stabilizers -- 18 Counting Orbits -- 19 Groups -- 20 The Sylow Theorems -- 21 Finitely Generated Abelian Groups -- 22 Row and Column Operations -- 23 Automorphisms -- 24 The Euclidean Group -- 25 Lattices and Point Groups -- 26 Wallpaper Patterns -- 27 Free Groups and Presentations -- 28 Trees and the Nielsen-Schreier Theorem.
520			_aGroups are important because they measure symmetry. This text, designed for undergraduate mathematics students, provides a gentle introduction to the highlights of elementary group theory. Written in an informal style, the material is divided into short sections each of which deals with an important result or a new idea. Throughout the book, the emphasis is placed on concrete examples, many of them geometrical in nature, so that finite rotation groups and the seventeen wallpaper groups are treated in detail alongside theoretical results such as Lagrange's theorem, the Sylow theorems, and the classification theorem for finitely generated abelian groups. A novel feature at this level is a proof of the Nielsen-Schreier theorem, using group actions on trees. There are more than three hundred exercises and approximately sixty illustrations to help develop the student's intuition.
650			_aGroup theory.
650			_aGroup Theory and Generalizations. _0https://scigraph.springernature.com/ontologies/product-market-codes/M11078
710			_aSpringerLink (Online service)
773			_tSpringer Nature eBook
776			_iPrinted edition: _z9781441930859
776			_iPrinted edition: _z9780387966755
776			_iPrinted edition: _z9781475740356
830			_aUndergraduate Texts in Mathematics, _x0172-6056
856			_uhttps://doi.org/10.1007/978-1-4757-4034-9
912			_aZDB-2-SMA
912			_aZDB-2-SXMS
912			_aZDB-2-BAE
999			_c9357 _d9357