字的有效性與群的冪零性

定　價：￥28.00

作　者：	李千路著
出版社：	北京郵電大學出版社
叢編項：
標　簽：	組合理論

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ISBN：	9787563519262	出版時間：	2009-05-01	包裝：	平裝
開本：	16開	頁數：	161	字數：

內容簡介

　　《字的有效性與群的冪零性》適合作為本科高年級學生的群論教材或參考資料，也可作為數學專業(yè)學生的雙語課教材。冪零群是介于交換群與可解群之間的一類群，在群論中占有十分重要的位置?！蹲值挠行耘c群的冪零性》研究群的廣義冪零性。冪零群被有限冪指數群的擴張群，是比冪零群范圍更廣的一類群；同時它們也遺傳了許多冪零群的良好性質，因而對這類群的研究具有十分重要的意義。作者在自己研究成果的基礎上，總結了多年來在該領域的一些典型成果，從群定律與群結構兩方面論述了群的冪零性?！蹲值挠行耘c群的冪零性》分兩部分。第一部分（2，3，4，5章）研究自由群及字（元素）的性質。第二部分研究群的結構。并著重研究了塌縮群，正定群，Milnor群，多項循環(huán)群sB一群等形態(tài)群的冪零性。

作者簡介

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圖書目錄

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