Hey man, I thought group theory sucks, but now I think group theory rocks. everything looks so beautifully consistent. I believe I should solve more problems in group theory rather than just dealing with the concepts abstractly.
I'll try to find how many solutions the equation x^{5}=e can have in S_{5}. then I'll try to guess how many solutions the equation x^{n}=e can have in S_{n} and will write down my thoughts here. it looks to be a good food for thought. Thank you guys for your helps, especially I like Serena.
One more question, Is it always possible to solve an equation like ax^{n}=b in S_{n}? When it's possible?
