| 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。 |
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 |
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