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Nilpotent groups and their automorphisms

Author: Evgenii I Khukhro
Publisher: Berlin ; New York : W. de Gruyter, 1993.
Series: De Gruyter expositions in mathematics, 8.
Edition/Format:   Print book : EnglishView all editions and formats
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Evgenii I Khukhro
ISBN: 3110136724 9783110136722
OCLC Number: 27642990
Description: xiii, 252 pages ; 25 cm.
Contents: pt. I. Linear Methods --
Ch. 1. Preliminaries --
1.1. Groups --
1.2. Rings and modules --
1.3. Lie rings --
1.4. Mappings, homomorphisms, automorphisms --
1.5. Group actions on a set --
1.6. Fixed points of automorphisms --
1.7. The Jordan normal form of a linear transformation of finite order --
1.8. Varieties and free groups --
1.9. Groups with operators --
1.10. Higman's Lemma --
Ch. 2. Nilpotent groups --
2.1. Commutators and commutator subgroups --
2.2. Definitions and basic properties of nilpotent groups --
2.3. Some sufficient conditions for soluble groups to be nilpotent --
2.4. The Schur-Baer Theorem and its converses --
2.5. Lower central series. Isolators --
2.6. Nilpotent groups without torsion --
2.7. Basic commutators and the collecting process --
2.8. Finite p-groups --
Ch. 3. Associated Lie rings --
3.1. Results on Lie rings analogous to theorems about groups --
3.2. Constructing a Lie ring from a group --
3.3. The Lie ring of a group of prime exponent --
3.4. The nilpotency of soluble Lie rings satisfying the Engel condition --
pt. II. Automorphisms --
Ch. 4. Lie rings admitting automorphisms with few fixed points --
4.1. Extending the ground ring --
4.2. Regular automorphisms of soluble Lie rings --
4.3. Regular automorphisms of Lie rings --
4.4. Almost regular automorphisms of prime order --
4.5. Comments --
Ch. 5. Nilpotent groups admitting automorphisms of prime order with few fixed points --
5.1. Regular automorphisms of prime order --
5.2. Nilpotent p-groups with automorphisms of order p --
5.3. Nilpotent groups with an almost regular automorphism of prime order --
5.4. Comments --
Ch. 6. Nilpotency in varieties of groups with operators --
6.1. Preliminary lemmas --
6.2. A nilpotency theorem --
6.3. A local nilpotency theorem --
6.4. Corollaries --
6.5. Comments --
Ch. 7. Splitting automorphisms of prime order and finite p-groups admitting a partition --
7.1. The connection between splitting automorphisms of prime order and finite p-groups admitting a partition --
7.2. The Restricted Burnside Problem for groups with a splitting automorphism of prime order --
7.3. The structure of finite p-groups admitting a partition and a positive solution of the Hughes problem --
7.4. Bounding the index of the Hughes subgroup --
7.5. Comments --
Ch. 8. Nilpotent p-groups admitting automorphisms of order p[superscript k] with few fixed points --
8.1. An application of the Mal'cev correspondence --
8.2. Powerful p-groups --
8.3. A weak bound for the derived length --
8.4. A strong bound for the derived length of a subgroup of bounded index.
Series Title: De Gruyter expositions in mathematics, 8.
Responsibility: by Evgenii I. Khukhro.
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