Question

This is a question from Abstract Algebra / Algebraic Structures

Consider H = {σ∈S5 | {σ(4),σ(5)} = {4,5} } of S5

Find all the left cosets of H.

This question could also be written as follows:

H ⊂ S5 where G is the set of all σ ∈ S5 that stabilize {4,5}. This means

G= {σ∈S5 | {σ(4),σ(5)}={4,5} . Find all the left cosets.

I am having a ton of difficulty understanding the notation and where to start/finish this problem. Any help would be appreciated.

Answer 1