The Theory of Classes of Groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2000
|
| Schriftenreihe: | Mathematics and Its Applications
505 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | One of the characteristics of modern algebra is the development of new tools and concepts for exploring classes of algebraic systems, whereas the research on individual algebraic systems (e. g. , groups, rings, Lie algebras, etc. ) continues along traditional lines. The early work on classes of algebras was concerned with showing that one class X of algebraic systems is actually contained in another class F. Modern research into the theory of classes was initiated in the 1930's by Birkhoff's work [1] on general varieties of algebras, and Neumann's work [1] on varieties of groups. A. I. Mal'cev made fundamental contributions to this modern development. In his reports [1, 3] of 1963 and 1966 to The Fourth All-Union Mathematics Conference and to another international mathematics congress, striking theories of classes of algebraic systems were presented. These were later included in his book [5]. International interest in the theory of formations of finite groups was aroused, and rapidly heated up, during this time, thanks to the work of Gaschiitz [8] in 1963, and the work of Carter and Hawkes [1] in 1967. The major topics considered were saturated formations, Fitting classes, and Schunck classes. A class of groups is called a formation if it is closed with respect to homomorphic images and subdirect products. A formation is called saturated provided that G E F whenever Gjip(G) E F. |
| Beschreibung: | 1 Online-Ressource (XI, 258 p) |
| ISBN: | 9789401140546 9789401057851 |
| DOI: | 10.1007/978-94-011-4054-6 |
Internformat
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| 490 | 1 | |a Mathematics and Its Applications |v 505 | |
| 500 | |a One of the characteristics of modern algebra is the development of new tools and concepts for exploring classes of algebraic systems, whereas the research on individual algebraic systems (e. g. , groups, rings, Lie algebras, etc. ) continues along traditional lines. The early work on classes of algebras was concerned with showing that one class X of algebraic systems is actually contained in another class F. Modern research into the theory of classes was initiated in the 1930's by Birkhoff's work [1] on general varieties of algebras, and Neumann's work [1] on varieties of groups. A. I. Mal'cev made fundamental contributions to this modern development. In his reports [1, 3] of 1963 and 1966 to The Fourth All-Union Mathematics Conference and to another international mathematics congress, striking theories of classes of algebraic systems were presented. These were later included in his book [5]. International interest in the theory of formations of finite groups was aroused, and rapidly heated up, during this time, thanks to the work of Gaschiitz [8] in 1963, and the work of Carter and Hawkes [1] in 1967. The major topics considered were saturated formations, Fitting classes, and Schunck classes. A class of groups is called a formation if it is closed with respect to homomorphic images and subdirect products. A formation is called saturated provided that G E F whenever Gjip(G) E F. | ||
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Datensatz im Suchindex
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| author | Wenbin, Guo |
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| dewey-full | 512.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-search | 512.2 |
| dewey-sort | 3512.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-011-4054-6 |
| format | Electronic eBook |
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| id | DE-604.BV042423927 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401140546 9789401057851 |
| language | English |
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| series2 | Mathematics and Its Applications |
| spelling | Wenbin, Guo Verfasser aut The Theory of Classes of Groups by Guo Wenbin Dordrecht Springer Netherlands 2000 1 Online-Ressource (XI, 258 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 505 One of the characteristics of modern algebra is the development of new tools and concepts for exploring classes of algebraic systems, whereas the research on individual algebraic systems (e. g. , groups, rings, Lie algebras, etc. ) continues along traditional lines. The early work on classes of algebras was concerned with showing that one class X of algebraic systems is actually contained in another class F. Modern research into the theory of classes was initiated in the 1930's by Birkhoff's work [1] on general varieties of algebras, and Neumann's work [1] on varieties of groups. A. I. Mal'cev made fundamental contributions to this modern development. In his reports [1, 3] of 1963 and 1966 to The Fourth All-Union Mathematics Conference and to another international mathematics congress, striking theories of classes of algebraic systems were presented. These were later included in his book [5]. International interest in the theory of formations of finite groups was aroused, and rapidly heated up, during this time, thanks to the work of Gaschiitz [8] in 1963, and the work of Carter and Hawkes [1] in 1967. The major topics considered were saturated formations, Fitting classes, and Schunck classes. A class of groups is called a formation if it is closed with respect to homomorphic images and subdirect products. A formation is called saturated provided that G E F whenever Gjip(G) E F. Mathematics Chemistry / Mathematics Group theory Algebra Logic, Symbolic and mathematical Group Theory and Generalizations Non-associative Rings and Algebras Order, Lattices, Ordered Algebraic Structures Mathematical Logic and Foundations Applications of Mathematics Math. Applications in Chemistry Chemie Mathematik Mathematics and Its Applications 505 (DE-604)BV008163334 505 https://doi.org/10.1007/978-94-011-4054-6 Verlag Volltext |
| spellingShingle | Wenbin, Guo The Theory of Classes of Groups Mathematics and Its Applications Mathematics Chemistry / Mathematics Group theory Algebra Logic, Symbolic and mathematical Group Theory and Generalizations Non-associative Rings and Algebras Order, Lattices, Ordered Algebraic Structures Mathematical Logic and Foundations Applications of Mathematics Math. Applications in Chemistry Chemie Mathematik |
| title | The Theory of Classes of Groups |
| title_auth | The Theory of Classes of Groups |
| title_exact_search | The Theory of Classes of Groups |
| title_full | The Theory of Classes of Groups by Guo Wenbin |
| title_fullStr | The Theory of Classes of Groups by Guo Wenbin |
| title_full_unstemmed | The Theory of Classes of Groups by Guo Wenbin |
| title_short | The Theory of Classes of Groups |
| title_sort | the theory of classes of groups |
| topic | Mathematics Chemistry / Mathematics Group theory Algebra Logic, Symbolic and mathematical Group Theory and Generalizations Non-associative Rings and Algebras Order, Lattices, Ordered Algebraic Structures Mathematical Logic and Foundations Applications of Mathematics Math. Applications in Chemistry Chemie Mathematik |
| topic_facet | Mathematics Chemistry / Mathematics Group theory Algebra Logic, Symbolic and mathematical Group Theory and Generalizations Non-associative Rings and Algebras Order, Lattices, Ordered Algebraic Structures Mathematical Logic and Foundations Applications of Mathematics Math. Applications in Chemistry Chemie Mathematik |
| url | https://doi.org/10.1007/978-94-011-4054-6 |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT wenbinguo thetheoryofclassesofgroups |