Intense Automorphisms of Finite Groups.

Format:

Book

Author/Creator:

Stanojkovski, Mima.

Series:

Memoirs of the American Mathematical Society

Memoirs of the American Mathematical Society ; v.273

Language:

English

Subjects (All):

Finite groups.

Automorphisms.

Nilpotent groups.

Physical Description:

1 online resource (132 pages)

Edition:

1st ed.

Place of Publication:

Providence : American Mathematical Society, 2021.

Summary:

"Let G be a group. An automorphism of G is called intense if it sends each subgroup of G to a conjugate; the collection of such automorphisms is denoted by Int(G). In the special case in which p is a prime number and G is a finite p-group, one can show that Int(G) is the semidirect product of a normal p-Sylow and a cyclic subgroup of order dividing p 1. In this paper we classify the finite p-groups whose groups of intense automorphisms are not themselves p-groups. It emerges from our investigation that the structure of such groups is almost completely determined by their nilpotency class: for p 3, they share a quotient, growing with their class, with a uniquely determined infinite 2-generated pro-p group"-- Provided by publisher.

Contents:

Cover

Title page

List of Symbols

Chapter 1. Introduction

Chapter 2. Coprime Actions

2.1. Actions through characters

2.2. Involutions

2.3. Jumps and width

Chapter 3. Intense Automorphisms

3.1. Basic properties

3.2. The main question

3.3. The abelian case

Chapter 4. Intensity of Groups of Class 2

4.1. Small commutator subgroup

4.2. More general setting

4.3. The extraspecial case

Chapter 5. Intensity of Groups of Class 3

5.1. Low intensity

5.2. Intensity given the automorphism

5.3. Constructing intense automorphisms

Chapter 6. Some Structural Restrictions

6.1. Normal subgroups

6.2. About the third width

6.3. A bound on the width

Chapter 7. Higher Nilpotency Classes

7.1. Class 4 and intensity

7.2. Class 5 and intensity

Chapter 8. A Disparity between the Primes

8.1. Regularity

8.2. Rank

8.3. A sharper bound on the width

Chapter 9. The Special Case of 3-groups

9.1. The cubing map

9.2. A specific example

9.3. Structures on vector spaces

9.4. Structures and free groups

9.5. Extensions

9.6. Constructing automorphisms

9.7. Intensity

Chapter 10. Obelisks

10.1. Some properties

10.2. Power maps and commutators

10.3. Framed obelisks

10.4. Subgroups of obelisks

Chapter 11. The Most Intense Chapter

11.1. The even case

11.2. The odd case, part I

11.3. The odd case, part II

11.4. Proving the main theorems

Chapter 12. High Class Intensity

12.1. A special case

12.2. The last exotic case

12.3. Proving the main theorem

Chapter 13. Intense Automorphisms of Profinite Groups

13.1. Some background

13.2. Properties and intensity

13.3. Non-abelian groups, part I

13.4. Two infinite groups

13.5. Non-abelian groups, part II

13.6. Proving the main theorems and more

Bibliography

Index

Back Cover.

Notes:

Description based on publisher supplied metadata and other sources.

Includes bibliographical references and index.

Other Format:

Print version: Stanojkovski, Mima Intense Automorphisms of Finite Groups

ISBN:

9781470468118

OCLC:

1284944685