Maximal solvable subgroups of finite classical groups:
This book studies maximal solvable subgroups of classical groups over finite fields. It provides the first modern account of Camille Jordan's classical results, and extends them, giving a classification of maximal irreducible solvable subgroups of general linear groups, symplectic groups, and o...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cham
Springer
[2024]
|
| Schriftenreihe: | Lecture notes in mathematics
2346 |
| Schlagworte: | |
| Zusammenfassung: | This book studies maximal solvable subgroups of classical groups over finite fields. It provides the first modern account of Camille Jordan's classical results, and extends them, giving a classification of maximal irreducible solvable subgroups of general linear groups, symplectic groups, and orthogonal groups over arbitrary finite fields. A subgroup of a group G is said to be maximal solvable if it is maximal among the solvable subgroups of G. The history of this notion goes back to Jordan’s Traité (1870), in which he provided a classification of maximal solvable subgroups of symmetric groups. The main difficulty is in the primitive case, which leads to the problem of classifying maximal irreducible solvable subgroups of general linear groups over a field of prime order. One purpose of this monograph is expository: to give a proof of Jordan’s classification in modern terms. More generally, the aim is to generalize these results to classical groups over arbitrary finite fields, and to provide other results of interest related to irreducible solvable matrix groups. The text will be accessible to graduate students and researchers interested in primitive permutation groups, irreducible matrix groups, and related topics in group theory and representation theory. The detailed introduction will appeal to those interested in the historical background of Jordan’s work |
| Beschreibung: | viii, 296 Seiten |
| ISBN: | 9783031629143 3031629159 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV049817174 | ||
| 003 | DE-604 | ||
| 005 | 20240816 | ||
| 007 | t | ||
| 008 | 240812s2024 |||| 00||| eng d | ||
| 020 | |a 9783031629143 |9 978-3-031-62914-3 | ||
| 020 | |a 3031629159 |9 3031629159 | ||
| 035 | |a (OCoLC)1452196957 | ||
| 035 | |a (DE-599)BVBBV049817174 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-188 |a DE-83 | ||
| 084 | |a SI 850 |0 (DE-625)143199: |2 rvk | ||
| 084 | |a 20Exx |2 msc/2020 | ||
| 100 | 1 | |a Korhonen, Mikko |d 1936-1991 |0 (DE-588)11954959X |4 aut | |
| 245 | 1 | 0 | |a Maximal solvable subgroups of finite classical groups |c Mikko Korhonen |
| 264 | 1 | |a Cham |b Springer |c [2024] | |
| 264 | 4 | |c © 2024 | |
| 300 | |a viii, 296 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 2346 | |
| 520 | 3 | |a This book studies maximal solvable subgroups of classical groups over finite fields. It provides the first modern account of Camille Jordan's classical results, and extends them, giving a classification of maximal irreducible solvable subgroups of general linear groups, symplectic groups, and orthogonal groups over arbitrary finite fields. A subgroup of a group G is said to be maximal solvable if it is maximal among the solvable subgroups of G. The history of this notion goes back to Jordan’s Traité (1870), in which he provided a classification of maximal solvable subgroups of symmetric groups. The main difficulty is in the primitive case, which leads to the problem of classifying maximal irreducible solvable subgroups of general linear groups over a field of prime order. One purpose of this monograph is expository: to give a proof of Jordan’s classification in modern terms. More generally, the aim is to generalize these results to classical groups over arbitrary finite fields, and to provide other results of interest related to irreducible solvable matrix groups. The text will be accessible to graduate students and researchers interested in primitive permutation groups, irreducible matrix groups, and related topics in group theory and representation theory. The detailed introduction will appeal to those interested in the historical background of Jordan’s work | |
| 653 | 0 | |a Solvable groups | |
| 653 | 0 | |a Finite groups | |
| 653 | 0 | |a Groupes résolubles | |
| 653 | 0 | |a Groupes finis | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-031-62915-0 |
| 830 | 0 | |a Lecture notes in mathematics |v 2346 |w (DE-604)BV000676446 |9 2346 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-035157431 | |
Datensatz im Suchindex
| _version_ | 1809767533069205504 |
|---|---|
| adam_text | |
| any_adam_object | |
| author | Korhonen, Mikko 1936-1991 |
| author_GND | (DE-588)11954959X |
| author_facet | Korhonen, Mikko 1936-1991 |
| author_role | aut |
| author_sort | Korhonen, Mikko 1936-1991 |
| author_variant | m k mk |
| building | Verbundindex |
| bvnumber | BV049817174 |
| classification_rvk | SI 850 |
| ctrlnum | (OCoLC)1452196957 (DE-599)BVBBV049817174 |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 cb4500</leader><controlfield tag="001">BV049817174</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20240816</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">240812s2024 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783031629143</subfield><subfield code="9">978-3-031-62914-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3031629159</subfield><subfield code="9">3031629159</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1452196957</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV049817174</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-188</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 850</subfield><subfield code="0">(DE-625)143199:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">20Exx</subfield><subfield code="2">msc/2020</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Korhonen, Mikko</subfield><subfield code="d">1936-1991</subfield><subfield code="0">(DE-588)11954959X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Maximal solvable subgroups of finite classical groups</subfield><subfield code="c">Mikko Korhonen</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cham</subfield><subfield code="b">Springer</subfield><subfield code="c">[2024]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2024</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">viii, 296 Seiten</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="490" ind1="1" ind2=" "><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">2346</subfield></datafield><datafield tag="520" ind1="3" ind2=" "><subfield code="a">This book studies maximal solvable subgroups of classical groups over finite fields. It provides the first modern account of Camille Jordan's classical results, and extends them, giving a classification of maximal irreducible solvable subgroups of general linear groups, symplectic groups, and orthogonal groups over arbitrary finite fields. A subgroup of a group G is said to be maximal solvable if it is maximal among the solvable subgroups of G. The history of this notion goes back to Jordan’s Traité (1870), in which he provided a classification of maximal solvable subgroups of symmetric groups. The main difficulty is in the primitive case, which leads to the problem of classifying maximal irreducible solvable subgroups of general linear groups over a field of prime order. One purpose of this monograph is expository: to give a proof of Jordan’s classification in modern terms. More generally, the aim is to generalize these results to classical groups over arbitrary finite fields, and to provide other results of interest related to irreducible solvable matrix groups. The text will be accessible to graduate students and researchers interested in primitive permutation groups, irreducible matrix groups, and related topics in group theory and representation theory. The detailed introduction will appeal to those interested in the historical background of Jordan’s work</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Solvable groups</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Finite groups</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Groupes résolubles</subfield></datafield><datafield tag="653" ind1=" " ind2="0"><subfield code="a">Groupes finis</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-3-031-62915-0</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Lecture notes in mathematics</subfield><subfield code="v">2346</subfield><subfield code="w">(DE-604)BV000676446</subfield><subfield code="9">2346</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-035157431</subfield></datafield></record></collection> |
| id | DE-604.BV049817174 |
| illustrated | Not Illustrated |
| indexdate | 2024-09-10T00:40:14Z |
| institution | BVB |
| isbn | 9783031629143 3031629159 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035157431 |
| oclc_num | 1452196957 |
| open_access_boolean | |
| owner | DE-188 DE-83 |
| owner_facet | DE-188 DE-83 |
| physical | viii, 296 Seiten |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Korhonen, Mikko 1936-1991 (DE-588)11954959X aut Maximal solvable subgroups of finite classical groups Mikko Korhonen Cham Springer [2024] © 2024 viii, 296 Seiten txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2346 This book studies maximal solvable subgroups of classical groups over finite fields. It provides the first modern account of Camille Jordan's classical results, and extends them, giving a classification of maximal irreducible solvable subgroups of general linear groups, symplectic groups, and orthogonal groups over arbitrary finite fields. A subgroup of a group G is said to be maximal solvable if it is maximal among the solvable subgroups of G. The history of this notion goes back to Jordan’s Traité (1870), in which he provided a classification of maximal solvable subgroups of symmetric groups. The main difficulty is in the primitive case, which leads to the problem of classifying maximal irreducible solvable subgroups of general linear groups over a field of prime order. One purpose of this monograph is expository: to give a proof of Jordan’s classification in modern terms. More generally, the aim is to generalize these results to classical groups over arbitrary finite fields, and to provide other results of interest related to irreducible solvable matrix groups. The text will be accessible to graduate students and researchers interested in primitive permutation groups, irreducible matrix groups, and related topics in group theory and representation theory. The detailed introduction will appeal to those interested in the historical background of Jordan’s work Solvable groups Finite groups Groupes résolubles Groupes finis Erscheint auch als Online-Ausgabe 978-3-031-62915-0 Lecture notes in mathematics 2346 (DE-604)BV000676446 2346 |
| spellingShingle | Korhonen, Mikko 1936-1991 Maximal solvable subgroups of finite classical groups Lecture notes in mathematics |
| title | Maximal solvable subgroups of finite classical groups |
| title_auth | Maximal solvable subgroups of finite classical groups |
| title_exact_search | Maximal solvable subgroups of finite classical groups |
| title_full | Maximal solvable subgroups of finite classical groups Mikko Korhonen |
| title_fullStr | Maximal solvable subgroups of finite classical groups Mikko Korhonen |
| title_full_unstemmed | Maximal solvable subgroups of finite classical groups Mikko Korhonen |
| title_short | Maximal solvable subgroups of finite classical groups |
| title_sort | maximal solvable subgroups of finite classical groups |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT korhonenmikko maximalsolvablesubgroupsoffiniteclassicalgroups |