LEADER 02926nam 22004815 450 001 9910971119003321 005 20240516010816.0 010 $a1-4612-0799-1 024 7 $a10.1007/978-1-4612-0799-3 035 $a(CKB)3400000000089274 035 $a(DE-He213)978-1-4612-0799-3 035 $a(MiAaPQ)EBC3073917 035 $a(PPN)238033511 035 $a(EXLCZ)993400000000089274 100 $a20121227d1995 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGroups and Representations /$fby J.L. Alperin, Rowen B. Bell 205 $a1st ed. 1995. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1995. 215 $a1 online resource (X, 196 p.) 225 1 $aGraduate Texts in Mathematics,$x0072-5285 ;$v162 320 $aIncludes bibliographical references and index. 327 $a1. Rudiments of Group Theory -- 1. Review -- 2. Automorphisms -- 3. Group Actions -- 2. The General Linear Group -- 4. Basic Structure -- 5. Parabolic Subgroups -- 6. The Special Linear Group -- 3. Local Structure -- 7. Sylow?s Theorem -- 8. Finite p-groups -- 9. The Schur-Zassenhaus Theorem -- 4. Normal Structure -- 10. Composition Series -- 11. Solvable Groups -- 5. Semisimple Algebras -- 12. Modules and Representations -- 13. Wedderburn Theory -- 6. Group Representations -- 14. Characters -- 15. The Character Table -- 16. Induction -- Appendix: Algebraic Integers and Characters -- List of Notation. 330 $aThe aim of this book is to provide a concise treatment of some topics from group theory and representation theory for a one term course. It focuses on the non-commutative side of the field emphasizing the general linear group as the most important group and example. The book will enable graduate students from every mathematical field, as well as strong undergraduates with an interest in algebra, to solidify their knowledge of group theory. The reader should have a familiarity with groups, rings, and fields, along with a solid knowledge of linear algebra. Close to 200 exercises of varying difficulty serve both to reinforce the main concept of the text and to expose the reader to additional topics. 410 0$aGraduate Texts in Mathematics,$x0072-5285 ;$v162 606 $aGroup theory 606 $aGroup Theory and Generalizations$3https://scigraph.springernature.com/ontologies/product-market-codes/M11078 615 0$aGroup theory. 615 14$aGroup Theory and Generalizations. 676 $a512.2 700 $aAlperin$b J.L$4aut$4http://id.loc.gov/vocabulary/relators/aut$054132 702 $aBell$b Rowen B.$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910971119003321 996 $aGroups and representations$9375584 997 $aUNINA