Finite Groups III:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1982
|
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
243 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Und dann erst kommt der "Ab -ge - sa. ng\' da. /3 der nidlt kurz und nicht zu la. ng, From "Die Meistersinger von Nürnberg", Richard Wagner This final volume is concerned with some of the developments of the subject in the 1960's. In attempting to determine the simple groups, the first step was to settle the conjecture of Burnside that groups of odd order are soluble. The proof that this conjecture was correct is much too long and complicated for presentation in this text, but a number of ideas in the early stages of it led to a local theory of finite groups, so me aspects of which are discussed in Chapter X. Much of this discussion is a con tinuation of the theory of the transfer (see Chapter IV), but we also introduce the generalized Fitting subgroup, which played a basic role in characterization theorems, that is, in descriptions of specific groups in terms of group-theoretical properties alone. One of the earliest and most important such characterizations was given for Zassenhaus groups; this is presented in Chapter XI. Characterizations in terms of the centralizer of an involution are of particular importance in view of the theorem of Brauer and Fowler. In Chapter XII, one such theorem is given, in which the Mathieu group 9J'l1l and PSL(3, 3) are characterized |
| Beschreibung: | 1 Online-Ressource (X, 456 p) |
| ISBN: | 9783642679971 9783642679995 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-642-67997-1 |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642679971 9783642679995 |
| issn | 0072-7830 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858344 |
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| physical | 1 Online-Ressource (X, 456 p) |
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| publishDate | 1982 |
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| publisher | Springer Berlin Heidelberg |
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| series2 | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |
| spelling | Huppert, Bertram Verfasser aut Finite Groups III by Bertram Huppert, Norman Blackburn Berlin, Heidelberg Springer Berlin Heidelberg 1982 1 Online-Ressource (X, 456 p) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 243 0072-7830 Und dann erst kommt der "Ab -ge - sa. ng\' da. /3 der nidlt kurz und nicht zu la. ng, From "Die Meistersinger von Nürnberg", Richard Wagner This final volume is concerned with some of the developments of the subject in the 1960's. In attempting to determine the simple groups, the first step was to settle the conjecture of Burnside that groups of odd order are soluble. The proof that this conjecture was correct is much too long and complicated for presentation in this text, but a number of ideas in the early stages of it led to a local theory of finite groups, so me aspects of which are discussed in Chapter X. Much of this discussion is a con tinuation of the theory of the transfer (see Chapter IV), but we also introduce the generalized Fitting subgroup, which played a basic role in characterization theorems, that is, in descriptions of specific groups in terms of group-theoretical properties alone. One of the earliest and most important such characterizations was given for Zassenhaus groups; this is presented in Chapter XI. Characterizations in terms of the centralizer of an involution are of particular importance in view of the theorem of Brauer and Fowler. In Chapter XII, one such theorem is given, in which the Mathieu group 9J'l1l and PSL(3, 3) are characterized Mathematics Group theory Group Theory and Generalizations Mathematik Blackburn, Norman Sonstige oth https://doi.org/10.1007/978-3-642-67997-1 Verlag Volltext |
| spellingShingle | Huppert, Bertram Finite Groups III Mathematics Group theory Group Theory and Generalizations Mathematik |
| title | Finite Groups III |
| title_auth | Finite Groups III |
| title_exact_search | Finite Groups III |
| title_full | Finite Groups III by Bertram Huppert, Norman Blackburn |
| title_fullStr | Finite Groups III by Bertram Huppert, Norman Blackburn |
| title_full_unstemmed | Finite Groups III by Bertram Huppert, Norman Blackburn |
| title_short | Finite Groups III |
| title_sort | finite groups iii |
| topic | Mathematics Group theory Group Theory and Generalizations Mathematik |
| topic_facet | Mathematics Group theory Group Theory and Generalizations Mathematik |
| url | https://doi.org/10.1007/978-3-642-67997-1 |
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