LEADER 04085nam 2200517 450 001 9910793246803321 005 20200520144314.0 010 $a3-11-059908-2 010 $a3-11-059919-8 024 7 $a10.1515/9783110599190 035 $a(CKB)4100000007205121 035 $a(MiAaPQ)EBC5625143 035 $a(DE-B1597)494732 035 $a(OCoLC)1078913511 035 $a(DE-B1597)9783110599190 035 $a(Au-PeEL)EBL5625143 035 $a(EXLCZ)994100000007205121 100 $a20190121d2019 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPeriodic locally compact groups $ea study of a class of totally disconnected topological groups /$fWolfgang Herfort, Karl H. Hofmann and Francesco G. Russo 210 1$aBerlin ;$aBoston :$cDe Gruyter,$d[2019] 215 $a1 online resource (358 pages) 225 1 $aDe Gruyter Studies in Mathematics ;$vVolume 71 311 $a3-11-059847-7 327 $tFrontmatter -- $tPreface -- $tContents -- $tOverview -- $tPart I: Background information on locally compact groups -- $tIntroduction -- $t1. Locally compact spaces and groups -- $t2. Periodic locally compact groups and their Sylow theory -- $t3. Abelian periodic groups -- $t4. Scalar automorphisms and the mastergraph -- $t5. Inductively monothetic groups -- $tPart II: Near abelian groups -- $tIntroduction -- $t6. The definition of near abelian groups -- $t7. Important consequences of the definitions -- $t8. Trivial near abelian groups -- $t9. The class of near abelian groups -- $t10. The Sylow structure of periodic nontrivial near abelian groups and their prime graphs -- $t11. A list of examples -- $tPart III: Applications -- $tIntroduction -- $t12. Classifying topologically quasihamiltonian groups -- $t13. Locally compact groups with a modular subgroup lattice -- $t14. Strongly topologically quasihamiltonian groups -- $tBibliography -- $tList of symbols -- $tIndex 330 $aThis authoritative book on periodic locally compact groups is divided into three parts: The first part covers the necessary background material on locally compact groups including the Chabauty topology on the space of closed subgroups of a locally compact group, its Sylow theory, and the introduction, classifi cation and use of inductively monothetic groups. The second part develops a general structure theory of locally compact near abelian groups, pointing out some of its connections with number theory and graph theory and illustrating it by a large exhibit of examples. Finally, the third part uses this theory for a complete, enlarged and novel presentation of Mukhin's pioneering work generalizing to locally compact groups Iwasawa's early investigations of the lattice of subgroups of abstract groups. Contents Part I: Background information on locally compact groups Locally compact spaces and groups Periodic locally compact groups and their Sylow theory Abelian periodic groups Scalar automorphisms and the mastergraph Inductively monothetic groups Part II: Near abelian groups The definition of near abelian groups Important consequences of the definitions Trivial near abelian groups The class of near abelian groups The Sylow structure of periodic nontrivial near abelian groups and their prime graphs A list of examples Part III: Applications Classifying topologically quasihamiltonian groups Locally compact groups with a modular subgroup lattice Strongly topologically quasihamiltonian groups 410 0$aDe Gruyter studies in mathematics ;$vVolume 71.$x0179-0986 606 $aGroup theory 606 $aLocally compact groups 615 0$aGroup theory. 615 0$aLocally compact groups. 676 $a512.2 700 $aHerfort$b Wolfgang$01527794 702 $aHofmann$b Karl Heinrich 702 $aRusso$b Francesco G. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910793246803321 996 $aPeriodic locally compact groups$93771009 997 $aUNINA