Wikipedia has separate pages for symmetric group and permutation group, but I don't understand what the difference between them is. A symmetric group on a set is the set of all bijections …

Oct 4, 2016 · I didn't find any good explanation how to perform multiplication on permutation group written in cyclic notation. For example, if $$ a= (1\,3\,5\,2),\quad b= (2\,5\,6 ...

Oct 11, 2020 · You already know the crucial pieces of information: the order of a cycle is its length, and the order of two group elements that commute is the least common multiple of …

Jan 22, 2024 · Answering simply: A permutation group G is transitive over a finite set X if for every x,y in X, there is a g in G such that y=gx, i.e. there is a g that maps x to y.

Feb 26, 2021 · So am I to assume that cyclic, alternating, lie groups, and sporadic groups are all actually permutation groups? As an additional question, if they all are, why identify finite simple …

Apr 21, 2013 · 0 This group is isomorphic to the 6 element dihedral group. Any element including a reflection will have order two. The product of two different such elements will be a pure …

The product (or composition) of permutation groups in two-line notation? Ask Question Asked 12 years, 1 month ago Modified 12 years, 1 month ago

Jul 30, 2022 · A permutation group is a subgroup of a symmetric group. Be careful, however, because Cayley's Theorem states that every group is isomorphic to a subgroup of a symmetric …

Aug 12, 2015 · What is a permutation representation in regard to group actions Ask Question Asked 10 years, 4 months ago Modified 2 years, 5 months ago

One side of the coin yields a valid permutation, and the other side doesn't. If you have been keeping track of how many swaps you did, then instead of flipping the coin, you can just …