Groups For Undergraduates
Seiten
1994
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-02-1557-6 (ISBN)
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-02-1557-6 (ISBN)
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The classical theorems of Sylow, Burnside, Schur and Frobenius are often used to show that the smallest single group has 60 elements. Here, the same theorems are used, but in combinations, with the result that any group with fewer elements is a semi-direct product of cyclic groups and a 2-group.
In these lecture notes the student learns basic theorems of the subject (due to Sylow, Burnside, Schur and Frobenius). More importantly, the student learns to use the theorems in various combinations, to discover for himself the groups of reasonably small order. In examples, presentations of the groups of order 1-31 and 33-42 are constructed.Once the groups are presented abstractly, the problem is not done: one needs to know how each abstract group may arise as a group of permutations or matrices. Theorems and techniques of representation theory are given which can do this for any group the student may have constructed in the earlier chapters — and the student ends up building the actual representations (not only the characters). In a series of examples, which the student may carry further, all the matrix representations are constructed for the groups of order less than 13.For students who are already familiar with homomorphisms, cosets, Lagrange's theorem, and finite abelian groups, the text may be used alone. For any group theory course, at least one text such as this one, containing lots of examples, is strongly recommended.The book is written in a lucid, straightforward style. The subject matter is presented from a student's perspective and constantly demands the student's involvement. Both these strategies are highly appropriate for a book of lecture notes and guarantee the student's understanding of the mathematical concepts.
In these lecture notes the student learns basic theorems of the subject (due to Sylow, Burnside, Schur and Frobenius). More importantly, the student learns to use the theorems in various combinations, to discover for himself the groups of reasonably small order. In examples, presentations of the groups of order 1-31 and 33-42 are constructed.Once the groups are presented abstractly, the problem is not done: one needs to know how each abstract group may arise as a group of permutations or matrices. Theorems and techniques of representation theory are given which can do this for any group the student may have constructed in the earlier chapters — and the student ends up building the actual representations (not only the characters). In a series of examples, which the student may carry further, all the matrix representations are constructed for the groups of order less than 13.For students who are already familiar with homomorphisms, cosets, Lagrange's theorem, and finite abelian groups, the text may be used alone. For any group theory course, at least one text such as this one, containing lots of examples, is strongly recommended.The book is written in a lucid, straightforward style. The subject matter is presented from a student's perspective and constantly demands the student's involvement. Both these strategies are highly appropriate for a book of lecture notes and guarantee the student's understanding of the mathematical concepts.
Introduction; Number-Theoretic Preliminaries; Semidirect Products; Presentations; Calculation of a List of the Groups of Order 1 - 31; Rewriting and Transfer; Classification of Certain Groups; Cohomology; More Cohomology; Linear Representations; Construction of the Linear Representations; Further Cohomology; Calculation of a List of the Representations of the Groups of Order 1 - 12.
| Erscheint lt. Verlag | 1.12.1994 |
|---|---|
| Verlagsort | Singapore |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| Sozialwissenschaften ► Pädagogik ► Erwachsenenbildung | |
| ISBN-10 | 981-02-1557-6 / 9810215576 |
| ISBN-13 | 978-981-02-1557-6 / 9789810215576 |
| Zustand | Neuware |
| Haben Sie eine Frage zum Produkt? |
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