LEADER 05537nam 22006493 450 001 9910968203903321 005 20231110223317.0 010 $a9781470468118$b(electronic bk.) 010 $z9781470450038 035 $a(MiAaPQ)EBC6822202 035 $a(Au-PeEL)EBL6822202 035 $a(CKB)20058043800041 035 $a(RPAM)22447283 035 $a(OCoLC)1284944685 035 $a(EXLCZ)9920058043800041 100 $a20211209d2021 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIntense Automorphisms of Finite Groups 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2021. 210 4$dİ2021. 215 $a1 online resource (132 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.273 311 08$aPrint version: Stanojkovski, Mima Intense Automorphisms of Finite Groups Providence : American Mathematical Society,c2021 9781470450038 320 $aIncludes bibliographical references and index. 327 $aCover -- 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. 330 $a"Let G be a group. An automorphism of G is called intense if it sends each subgroup of G to a conjugate; the collection of such automorphisms is denoted by Int(G). In the special case in which p is a prime number and G is a finite p-group, one can show that Int(G) is the semidirect product of a normal p-Sylow and a cyclic subgroup of order dividing p 1. In this paper we classify the finite p-groups whose groups of intense automorphisms are not themselves p-groups. It emerges from our investigation that the structure of such groups is almost completely determined by their nilpotency class: for p 3, they share a quotient, growing with their class, with a uniquely determined infinite 2-generated pro-p group"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aFinite groups 606 $aAutomorphisms 606 $aNilpotent groups 606 $aGroup theory and generalizations -- Abstract finite groups -- Nilpotent groups, $p$-groups$2msc 606 $aGroup theory and generalizations -- Abstract finite groups -- Automorphisms$2msc 606 $aGroup theory and generalizations -- Special aspects of infinite or finite groups -- Automorphism groups of groups$2msc 606 $aGroup theory and generalizations -- Structure and classification of infinite or finite groups -- Limits, profinite groups$2msc 606 $aGroup theory and generalizations -- Structure and classification of infinite or finite groups -- Automorphisms of infinite groups$2msc 615 0$aFinite groups. 615 0$aAutomorphisms. 615 0$aNilpotent groups. 615 7$aGroup theory and generalizations -- Abstract finite groups -- Nilpotent groups, $p$-groups. 615 7$aGroup theory and generalizations -- Abstract finite groups -- Automorphisms. 615 7$aGroup theory and generalizations -- Special aspects of infinite or finite groups -- Automorphism groups of groups. 615 7$aGroup theory and generalizations -- Structure and classification of infinite or finite groups -- Limits, profinite groups. 615 7$aGroup theory and generalizations -- Structure and classification of infinite or finite groups -- Automorphisms of infinite groups. 676 $a512/.23 686 $a20D15$a20D45$a20F28$a20E18$a20E36$2msc 700 $aStanojkovski$b Mima$01800256 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910968203903321 996 $aIntense Automorphisms of Finite Groups$94344968 997 $aUNINA