本书共分14个章节，作者总结了其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。本书分两部分。第一部分研究自由群及字(元素)的性质。第二部分研究群的结构。该书可供各大专院校作为教材使用，也可供从事相关工作的人员作为参考用书使用。

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。本书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。本书分两部分。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-群等形态群的幂零性。

该书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。

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 Cp■C

 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