✳flâneur — a map of the web's best reading

Symmetric group S4 - Wikiversity

en.wikiversity.org · 1,657 words · saved by 1 readers

The small table on the left shows the permuted elements, and inversion vectors (which are reflected factorial numbers) below them. Another column shows the inversion sets, ordered like . (When a dot with the numbers i,j is marked red, than the elements on places i,j are out of their natural order.) The digit sums of the inversion vectors (or factorial numbers) and the cardinalities of the inversion sets are equal. They form the sequence A034968. A permutation and its corresponding digit sum have the same parity. The big table on the right is the Cayley table of S4. It could also be given as the matrix multiplication table of the shown permutation matrices. (Compare multiplication table for S3) There are 30 subgroups of S4, including the group itself and the 10 small subgroups. Every group has as many small subgroups as neutral elements on the main diagonal: The trivial group and two-element groups Z2. These small subgroups are not counted in the following list. The subgroups of every

Symmetric group S4 - Wikiversity Jump to content From Wikiversity Cycle graph of S 4 The symmetric group S 4 {\displaystyle S_{4}} is the group of all permutations of 4 elements. It has 4 ! = 4 ⋅ 3 ⋅ 2 ⋅ 1 = 24 {\displaystyle 4!=4\cdot 3\cdot 2\cdot 1=24} elements and is not abelian . Even permutations are white: the identity eight 3- cycles three double- transpositions (in bold typeface) Odd permutations are colored: six transpositions (green) six 4-cycles (orange) The small table on the left shows the permuted elements, and inversion vectors (which are reflected factoria

Explore this link on the map →

related reading