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    Permutation Groups

    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...
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    Alternating Group

    For any elements σ, τ ∈ Sn, show that στσ-1τ-1 ∈ An.
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    Permutation Groups

    Homework Statement 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.
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    Abstract Algebra question

    Homework 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...