6.4: Reading Questions
State Lagrange's Theorem in your own words.
Determine the left cosets of \(\langle 3 \rangle\) in \(\mathbb Z_9\text{.}\)
The set \(\{(), (1\,2)(3\,4), (1\,3)(2\,4), (1\,4)(2\,3)\}\) is a subgroup of \(S_4\text{.}\) What is its index in \(S_4\text{?}\)
Suppose \(G\) is a group of order 29. Describe \(G\text{.}\)
The number \(p=137909\) is prime. Explain how to compute \(57^{137909}\pmod{137909}\) without a calculator.