AATA Reading Questions

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Reading Questions 6.4 Reading Questions

1.

State Lagrange's Theorem in your own words.

2.

Determine the left cosets of $\langle 3 \rangle$ in $\mathbb Z_9\text{.}$

3.

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 $S_4\text{?}$

4.

Suppose $G$ is a group of order 29. Describe $G\text{.}$

5.

The number $p=137909$ is prime. Explain how to compute $57^{137909}\pmod{137909}$ without a calculator.

Abstract Algebra: Theory and Applications

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Reading Questions 6.4 Reading Questions

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