Subject: Abstract Algebra
Please help me out with these problems through proofing. There are two parts to it.
Suppose G is a group, with a belong to G.
a. Prove that a^ma^n = a^m+n for all natural numbers m and n. Hint: Fix n belong to N. Then prove by mathematical induction on m.
b. Prove that (a^m)^n = a^mn for all natural numbers m and n.