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字的有效性与群的幂零性
作者：李千路 著
出版社：北京邮电大学出版社
出版时间：2009-05-01
ISBN：9787563519262
定价：¥28.00
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内容简介
《字的有效性与群的幂零性》适合作为本科高年级学生的群论教材或参考资料，也可作为数学专业学生的双语课教材。幂零群是介于交换群与可解群之间的一类群，在群论中占有十分重要的位置。《字的有效性与群的幂零性》研究群的广义幂零性。幂零群被有限幂指数群的扩张群，是比幂零群范围更广的一类群；同时它们也遗传了许多幂零群的良好性质，因而对这类群的研究具有十分重要的意义。作者在自己研究成果的基础上，总结了多年来在该领域的一些典型成果，从群定律与群结构两方面论述了群的幂零性。《字的有效性与群的幂零性》分两部分。第一部分（2，3，4，5章）研究自由群及字（元素）的性质。第二部分研究群的结构。并着重研究了塌缩群，正定群，Milnor群，多项循环群sB一群等形态群的幂零性。
作者简介
暂缺《字的有效性与群的幂零性》作者简介
目录
Chapter 1 Preface
Chapter 2 Fundamental Concept Ⅰ： Free Groups
2.1 Free Groups in a Class
2.2 Words
2.3 （Absolutely） Free Groups
Chapter 3 Words in the Free Group F2
3.1 Commutator Remainders
3.2 Efficient Words
3.3 Homomorphie Images of Words
3.4 Homomorphie Invariant
3.5 Homomorphie Properties
3.6 Efficiency of Words
Chapter 4 General Words
4.1 Notions and Notations
4.2 Standard Forms of Words
4.3 Uniqueness of Standard Forms
4.4 Criterion of Efficiency
Chapter 5 Properties of the Standard Exponents of Words
5.1 Words of the Form ω（x1m1，…，xnmn）
5.2 Words of the Form ω1l1…ωlss
5.3 Words to and to ωσ
Chapter 6 Fundamental Concept ll：Nilpotent Groups
6.1 Nilpotenee of Groups
6.2 Preliminary Properties of Nilpotent Groups
6.3 The Most Important Subclasses of Nilpotent Groups
6.3.1 Finite Nilpotent Groups
6.3.2 Finitely Generated Nilpotent Groups
6.3.3 Torsion-free Nilpotent Group
6.4 Generalizations of Nilpotence
6.4.1 Local Nilpotence
6.4.2 The Normalizer C0ndition
Chapter 7 Collapsing Groups
7.1 Engel Identities
7.2 Collapsing Conditions
7.3 Collapsing Laws for Almost Nilpotence
7.4 Residually Finite Groups
Chapter 8 Groups Satisfying Positive Words
8.1 Some Properties
8.2 Nilpotenee
8.3 SB-groups
Chapter 9 Milnor Groups and Groups Satisfying Efficient Words
9.1 Groups Satisfying Efficient Words
9.1.1 Efficient Conditions
9.1.2 Efficiency and Nilpotenee
9.2 Milnor Groups
9.3 Finite f-Milnor Groups
9.3.1 Finite Soluble f-Milnor Groups
9.3.2 Finite Nilpotent Groups in My
9.3.3 Finite f-Milnor Groups
Chapter 10 Polycyclic Groups
10.1 Properties of Polyeyelie Groups
10.2 Polycyelic Conditions for Nilpotence
10.3 Polycyelic Groups in Varieties
10.4 Nilpotent Polycyclic Groups
Chapter 11 Varieties of Groups
11.1 Words and Varieties
11.2 Nilpotent Conditions
11.3 Varieties with Finite Basis
11.4 Variety A2
Chapter 12 Metabelian Suhvarieties of Groups
12.1 Variety ApA
12.2 Variety ApA
12.2.1 Some Lemmas
12.2.2 Milnor Groups and Nilpotence
12.3 Variety AA
Chapter 13 Finitely Generated f-Milnor Groups
13.1 Weak Milnor Classes
13.2 Structure off-Milnor Groups
13.3 Strong Milnor Classes
Chapter 14 Criteria for Almost Nilpotence
14.1 Laws for CpC
14.2 Varieties Being Almost Nilpotent
14.3 Some Preliminary Results of Groups
14.3.1 Commutator Groups
14.3.2 Isolators of Subgroups
14.4 Torsion-by-Nilpotent Groups
14.5 Example
Bibliography
Chapter 2 Fundamental Concept Ⅰ： Free Groups
2.1 Free Groups in a Class
2.2 Words
2.3 （Absolutely） Free Groups
Chapter 3 Words in the Free Group F2
3.1 Commutator Remainders
3.2 Efficient Words
3.3 Homomorphie Images of Words
3.4 Homomorphie Invariant
3.5 Homomorphie Properties
3.6 Efficiency of Words
Chapter 4 General Words
4.1 Notions and Notations
4.2 Standard Forms of Words
4.3 Uniqueness of Standard Forms
4.4 Criterion of Efficiency
Chapter 5 Properties of the Standard Exponents of Words
5.1 Words of the Form ω（x1m1，…，xnmn）
5.2 Words of the Form ω1l1…ωlss
5.3 Words to and to ωσ
Chapter 6 Fundamental Concept ll：Nilpotent Groups
6.1 Nilpotenee of Groups
6.2 Preliminary Properties of Nilpotent Groups
6.3 The Most Important Subclasses of Nilpotent Groups
6.3.1 Finite Nilpotent Groups
6.3.2 Finitely Generated Nilpotent Groups
6.3.3 Torsion-free Nilpotent Group
6.4 Generalizations of Nilpotence
6.4.1 Local Nilpotence
6.4.2 The Normalizer C0ndition
Chapter 7 Collapsing Groups
7.1 Engel Identities
7.2 Collapsing Conditions
7.3 Collapsing Laws for Almost Nilpotence
7.4 Residually Finite Groups
Chapter 8 Groups Satisfying Positive Words
8.1 Some Properties
8.2 Nilpotenee
8.3 SB-groups
Chapter 9 Milnor Groups and Groups Satisfying Efficient Words
9.1 Groups Satisfying Efficient Words
9.1.1 Efficient Conditions
9.1.2 Efficiency and Nilpotenee
9.2 Milnor Groups
9.3 Finite f-Milnor Groups
9.3.1 Finite Soluble f-Milnor Groups
9.3.2 Finite Nilpotent Groups in My
9.3.3 Finite f-Milnor Groups
Chapter 10 Polycyclic Groups
10.1 Properties of Polyeyelie Groups
10.2 Polycyelic Conditions for Nilpotence
10.3 Polycyelic Groups in Varieties
10.4 Nilpotent Polycyclic Groups
Chapter 11 Varieties of Groups
11.1 Words and Varieties
11.2 Nilpotent Conditions
11.3 Varieties with Finite Basis
11.4 Variety A2
Chapter 12 Metabelian Suhvarieties of Groups
12.1 Variety ApA
12.2 Variety ApA
12.2.1 Some Lemmas
12.2.2 Milnor Groups and Nilpotence
12.3 Variety AA
Chapter 13 Finitely Generated f-Milnor Groups
13.1 Weak Milnor Classes
13.2 Structure off-Milnor Groups
13.3 Strong Milnor Classes
Chapter 14 Criteria for Almost Nilpotence
14.1 Laws for CpC
14.2 Varieties Being Almost Nilpotent
14.3 Some Preliminary Results of Groups
14.3.1 Commutator Groups
14.3.2 Isolators of Subgroups
14.4 Torsion-by-Nilpotent Groups
14.5 Example
Bibliography
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