20.500.12556/DKUM-17654 Podgrupe simetrične grupe S5 Subgroups of symmetric group S5 V diplomskem delu najprej obravnavamo grupe in njihove lastnosti, ter le-te ponazorimo na primerih. Nato definiramo še pojme direktni produkt, homomorfizem in izomorfizem, ki jih uporabimo v osrednjem delu diplome. Predstavimo še ciklične in diedrske grupe, ki v tretjem poglavju nastopajo kot podgrupe simetrične grupe S5 . V drugem poglavju so podrobno predstavljene simetrične grupe in njihove poglavitne lastnosti s primeri. V zadnjem, tretjem delu diplome pa opišemo vse podgrupe grupe S5 in izomorfizme med njimi. Razdelimo jih na maksimalne in nemaksimalne, ter pokažemo, da drugih podgrup S5 ne vsebuje. In the diploma work, firstly, we deal with groups and their properties. The latest we present with some examples. Then we define the following concepts: direct product, homomorphism and isomorphism. We use these concepts in the central part of the diploma work as well. We also present cyclic and dihedral groups. In chapter 3, they take a role of subgroups of the symmetric group S5 . In chapter 2, symmetric groups and their main properties, based on the examples, are presented. In the last part of the diploma work we describe all of the subgroups of the group S5, and the isomorphisms between them. Then we divide them to maximal and non-maximal subgroups. We also show, that there are no other subgroups in S5 . permutacija cikel transpozicija množenje permutacij grupa podgrupa moč podgrupe maksimalna podgrupa izomorfizem a permutation a cycle a transposition permutation multiplication a group a subgroup subgroup power a maximal subgroup isomorphism true true false [B. Čakš] Slovenski jezik Angleški jezik Diplomsko delo 2011-03-05 12:29:03 2011-04-04 11:21:12 2022-04-13 09:41:35 2023-12-22 03:40:39 2011 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 51(043.2) 18245384 URN:SI:UM:DK:HNH3MRRI UNI_Caks_Branka_2011.pdf UNI_Caks_Branka_2011.pdf 1 9D5C383F4C2F33F4CD3B74411992C5FD 27dc633b779aa8e4062fe190902593a79a5f200df8f2717f5fdbdd6968da35fd f18101b6-7c04-11eb-bb7a-00155d0001ca 20.500.12556/dkum/74e1e14b-3d84-4674-929c-514fb24bbc4b https://dk.um.si/Dokument.php?lang=slv&id=20706 Fakulteta za naravoslovje in matematiko 0 0 0