Intense Automorphisms of Finite Groups

• Autore: Stanojkovski Mima
• Pubblicazione: Providence : , : American Mathematical Society, , 2021; ©2021
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (132 pages)
• Disciplina: 512/.23
• Soggetto topico: Finite groups; Automorphisms; Nilpotent groups; Group theory and generalizations -- Abstract finite groups -- Nilpotent groups, $p$-groups; Group theory and generalizations -- Abstract finite groups -- Automorphisms; Group theory and generalizations -- Special aspects of infinite or finite groups -- Automorphism groups of groups; Group theory and generalizations -- Structure and classification of infinite or finite groups -- Limits, profinite groups; Group theory and generalizations -- Structure and classification of infinite or finite groups -- Automorphisms of infinite groups
• Classificazione: 20D1520D4520F2820E1820E36
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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.
• Sommario/riassunto: "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"--
• Titolo autorizzato: Intense Automorphisms of Finite Groups
• ISBN: 9781470468118; 9781470450038
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910968203903321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society