Introduction to group characters:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Cambridge u.a.
Cambridge Univ. Pr.
1987
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 227 S. |
| ISBN: | 052133246X 052133781X |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV002128549 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | t | ||
| 008 | 890928s1987 |||| 00||| ger d | ||
| 020 | |a 052133246X |9 0-521-33246-X | ||
| 020 | |a 052133781X |9 0-521-33781-X | ||
| 035 | |a (OCoLC)13902690 | ||
| 035 | |a (DE-599)BVBBV002128549 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a ger | |
| 049 | |a DE-91 |a DE-384 |a DE-739 |a DE-11 | ||
| 050 | 0 | |a QA171 | |
| 082 | 0 | |a 512/.22 |2 19 | |
| 084 | |a SK 260 |0 (DE-625)143227: |2 rvk | ||
| 084 | |a MAT 202f |2 stub | ||
| 100 | 1 | |a Ledermann, Walter |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to group characters |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Cambridge u.a. |b Cambridge Univ. Pr. |c 1987 | |
| 300 | |a X, 227 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Caractères de groupes | |
| 650 | 7 | |a Caractères de groupes |2 ram | |
| 650 | 7 | |a Groupes finis |2 ram | |
| 650 | 4 | |a Groupes, Théorie des | |
| 650 | 4 | |a Characters of groups | |
| 650 | 0 | 7 | |a Charakter |g Gruppentheorie |0 (DE-588)4158438-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Gruppentheorie |0 (DE-588)4072157-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Charakter |g Gruppentheorie |0 (DE-588)4158438-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Gruppentheorie |0 (DE-588)4072157-7 |D s |
| 689 | 1 | |8 1\p |5 DE-604 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001395806&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-001395806 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Record in the Search Index
| _version_ | 1804116582304055296 |
|---|---|
| adam_text | CONTENTS
Preface to the second edition page vii
Preface ix
1 GROUP REPRESENTATIONS 1
1.1 Introduction 1
1.2 G modules 5
1.3 Characters 9
1.4 Reducibility 10
1.5 Permutation representations 17
1.6 Complete reducibility 20
1.7 Schur s Lemma 24
1.8 The commutant (endomorphism) algebra 27
2 ELEMENTARY PROPERTIES OF
GROUP CHARACTERS 37
2.1 Orthogonality relations 37
2.2 The group algebra 42
2.3 The character table 49
2.4 Finite Abelian groups 52
2.5 The lifting process 57
2.6 Linear characters 62
3 INDUCED CHARACTERS 69
3.1 Induced representations 69
3.2 The reciprocity law 73
3.3 The alternating group As 75
3.4 Normal subgroups 79
3.5 Tensor products 83
3.6 Mackey s Theorem 94
4 PERMUTATION GROUPS 101
4.1 Transitive groups . 101
4.2 The symmetric group 106
4.3 Induced characters of Sn 108
CONTENTS
4.4 Generalised characters 110
4.5 Skew symmetric polynomials 111
4.6 Generating functions 114
4.7 Orthogonality 116
4.8 The degree formula 120
4.9 Schur functions 123
4.10 Conjugate partitions 128
4.11 The characters of S5 135
5 GROUP THEORETICAL APPLICATIONS 141
5.1 Algebraic numbers 141
5.2 Representations of the group algebra 146
5.3 Burnside s (p, q) theorem 148
5.4 Frobenius groups 152
6 ARITHMETIC PROPERTIES OF
GROUP CHARACTERS 160
6.1 Real character values 160
6.2 Rational character values 161
6.3 A congruence property 165
7 REAL REPRESENTATIONS 170
7.1 Statement of the problem 170
7.2 Quadratic forms 171
7.3 Orthogonal representations 173
7.4 Bilinear invariants 177
7.5 The character criterion 181
APPENDIX 186
A.I A generalisation of Vandermonde s determinant 186
A.2 The alternant quotient 188
A.3 Jacobi s Theorem on inverse matrices 191
A.4 Quadratic forms 194
A.5 Congruence relations in an algebraic number field 197
List of character tables 205
Solutions 206
Bibliography 224
Index 226
|
| any_adam_object | 1 |
| author | Ledermann, Walter |
| author_facet | Ledermann, Walter |
| author_role | aut |
| author_sort | Ledermann, Walter |
| author_variant | w l wl |
| building | Verbundindex |
| bvnumber | BV002128549 |
| callnumber-first | Q - Science |
| callnumber-label | QA171 |
| callnumber-raw | QA171 |
| callnumber-search | QA171 |
| callnumber-sort | QA 3171 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 260 |
| classification_tum | MAT 202f |
| ctrlnum | (OCoLC)13902690 (DE-599)BVBBV002128549 |
| dewey-full | 512/.22 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.22 |
| dewey-search | 512/.22 |
| dewey-sort | 3512 222 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01730nam a2200481 c 4500</leader><controlfield tag="001">BV002128549</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">890928s1987 |||| 00||| ger d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">052133246X</subfield><subfield code="9">0-521-33246-X</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">052133781X</subfield><subfield code="9">0-521-33781-X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)13902690</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV002128549</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">ger</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA171</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">512/.22</subfield><subfield code="2">19</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 260</subfield><subfield code="0">(DE-625)143227:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 202f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ledermann, Walter</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Introduction to group characters</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge u.a.</subfield><subfield code="b">Cambridge Univ. Pr.</subfield><subfield code="c">1987</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">X, 227 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Caractères de groupes</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Caractères de groupes</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Groupes finis</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Groupes, Théorie des</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Characters of groups</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Charakter</subfield><subfield code="g">Gruppentheorie</subfield><subfield code="0">(DE-588)4158438-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Gruppentheorie</subfield><subfield code="0">(DE-588)4072157-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Charakter</subfield><subfield code="g">Gruppentheorie</subfield><subfield code="0">(DE-588)4158438-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Gruppentheorie</subfield><subfield code="0">(DE-588)4072157-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001395806&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-001395806</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV002128549 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:40:48Z |
| institution | BVB |
| isbn | 052133246X 052133781X |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001395806 |
| oclc_num | 13902690 |
| open_access_boolean | |
| owner | DE-91 DE-BY-TUM DE-384 DE-739 DE-11 |
| owner_facet | DE-91 DE-BY-TUM DE-384 DE-739 DE-11 |
| physical | X, 227 S. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Cambridge Univ. Pr. |
| record_format | marc |
| spelling | Ledermann, Walter Verfasser aut Introduction to group characters 2. ed. Cambridge u.a. Cambridge Univ. Pr. 1987 X, 227 S. txt rdacontent n rdamedia nc rdacarrier Caractères de groupes Caractères de groupes ram Groupes finis ram Groupes, Théorie des Characters of groups Charakter Gruppentheorie (DE-588)4158438-7 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Charakter Gruppentheorie (DE-588)4158438-7 s DE-604 Gruppentheorie (DE-588)4072157-7 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001395806&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ledermann, Walter Introduction to group characters Caractères de groupes Caractères de groupes ram Groupes finis ram Groupes, Théorie des Characters of groups Charakter Gruppentheorie (DE-588)4158438-7 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4158438-7 (DE-588)4072157-7 |
| title | Introduction to group characters |
| title_auth | Introduction to group characters |
| title_exact_search | Introduction to group characters |
| title_full | Introduction to group characters |
| title_fullStr | Introduction to group characters |
| title_full_unstemmed | Introduction to group characters |
| title_short | Introduction to group characters |
| title_sort | introduction to group characters |
| topic | Caractères de groupes Caractères de groupes ram Groupes finis ram Groupes, Théorie des Characters of groups Charakter Gruppentheorie (DE-588)4158438-7 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Caractères de groupes Groupes finis Groupes, Théorie des Characters of groups Charakter Gruppentheorie Gruppentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001395806&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ledermannwalter introductiontogroupcharacters |