20.500.12556/DKUM-67531 p-grupe p-groups Cilj magistrskega dela je spoznati p-grupe in z njimi povezane izreke Sylowa. Najprej obravnavamo osnovne pojme teorije grup, ki jih potrebujemo za razumevanje magistrskega dela. Spoznamo enačbo razreda in proučimo morfizme grup ter vpeljemo direktni produkt grup. Največjo pozornost namenimo p-grupam, izrekom Sylowa in njihovi uporabi v klasifikaciji grup majhnih redov. Obravnavamo končne p-grupe in njihove najpomembnejše lastnosti, nekaj časa pa namenimo tudi neskončnim p-grupam, ki jih spoznavamo na primeru Prüferjevih grup. The aim of the master thesis is to present p-groups and the related Sylow theorems. In our master thesis we examine basic concepts of group theory which are needed for understanding the concepts that follow. We define the class equation, study group morphisms and introduce the direct product of groups. We pay the greatest attention to p-groups, the Sylow theorems and their use in the classification of groups of small orders. We examine finite p-groups and their most important properties. We also devote some of the time to infinite p-groups which we get to know on the example of Prüfer groups. p-grupe izreki Sylowa enačba razreda izomorfizem grup direktni produkt grup grupe majhnih redov Prüferjeve grupe p-groups Sylow theorems class equation group isomorphism direct product of groups groups of small orders Prüfer groups true true false [U. Bezjak] Slovenski jezik Angleški jezik Magistrsko delo/naloga 2017-08-22 13:46:38 2017-09-19 09:29:56 2022-08-01 14:05:40 2019-07-11 16:23:29 2017 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.54(043.2) 23323400 URN:SI:UM:DK:XNI1VAWW MAG_Bezjak_Urska_2017.pdf MAG_Bezjak_Urska_2017.pdf 1 104E52FB49214604FEB393C561295257 74dc7c50ca1d390af45f69cefa1d981fd4fab8f552ee6650f700cdb322c40397 8eebfe49-7c0e-11eb-bb7a-00155d0001ca 20.500.12556/dkum/5265a901-e921-44fc-bb8e-e0a90caf8e5a https://dk.um.si/Dokument.php?lang=slv&id=115985 Fakulteta za naravoslovje in matematiko 0 0 0