Generating $S_7$ only by $7$-cycles

Question

Do all the $7$-cycles in $S_7$ generate $S_7$? How?

Can we generalize the idea?

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(Edited)

I found a new idea:

Assume $$\sigma = (x_1,x_2,x_3,x_4,x_5,x_6,x_7)$$ and $$\tau=(x_7,x_6,x_5,x_4,x_3,x_1,x_2)$$ Now: $$\sigma\tau=(x_1,x_2,x_3)$$ So, we can generate all $3$-cycles.

Theorem: Let $n ≥ 3$. Prove that $A_n$ can be generated by all the $3$-cycles in $S_n$.

What should I do for $S_n - A_n$?

Thank you for your answers.

Answer 1

No. A $7-$cycle has parity $+1$, therefore you cannot reach a transposition just using $7-$cycles.