Group Theory - 북프라이스

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· 제목 : Group Theory (Paperback)
· 분류 : 외국도서 > 과학/수학/생태 > 수학 > 군론
· ISBN : 9781792478925
· 쪽수 : 277쪽
· 출판일 : 2021-08-30

Basic Theory on Groups
1.1 Basic properties of groups
1.2 Groups of permutations
1.3 Isomorphism theorems
1.4 Commutator subgroups and dihedral groups
1.5 Exercises
2. Group Actions
2.1 Group action on a set
2.2 Applications of -sets to counting
2.3 Symmetries of the regular polyhedrons
2.4 Simplegroups
2.5 Exercises
3. Jordan–Holder Theorem and Sylow Theorems
3.1 Series of groups
3.2 Composition series of groups
3.3 Finite –groups
3.4 Sylowtheorems
3.5 Applications of the Sylow Theorems
3.6 Exercises
4. Free Groups
4.1 Free abelian groups
4.2 Freegroups
4.3 Group presentations
4.4 Exercises
5. Solvable Groups
5.1 Basic properties of solvable groups
5.2 Finite solvable groups
5.3 Hall subgroups
5.4 Sylow systems and Sylow bases
5.5 Exercises
6. Nilpotent Groups
6.1 Basic properties of nilpotent groups
6.2 Frattini subgroups
6.3 Exercises
7. Representations of Groups
7.1 Definitions and examples
7.2 Subrepresentations, quotient representations, and homomorphisms
7.3 The methods of constructing representations
7.4 Irreducible representations, completely reducible representations
7.5 Maschke's Theorem
7.6 Exercises
Sample Solutions
Appendix A: Equivalence Relations and Kuratowski–Zorn Lemma
References
Index