Is it really that simple? lol This is what I was thinking, but I wasn't sure how to connect the idea to permutations. Can I just say "a is an even permutation" and "b is an even permutation" thus "a*b is also an even permutation"? Because, if this is true and if I assume that a and b are...
Show that if G is any group of permutations, then the set of all even permutations in G forms a subgroup of G.
I am not sure where to start - I know there is a proposition that states this to be true, but I know that is not enough to prove this statement.
Let G be a group with pk elements, where p is a prime number and k is greater than or equal to 1. Prove that G has a subgroup of order p.
The Attempt at a Solution
I attempted to prove this by showing that the conditions for a set to be subgroup form a subgroup of order...