# Abstract algebra questions and answers

Recent questions in Abstract algebra
Marvin Mccormick 2021-02-08 Answered

### Let $$\mathbb{R}$$ sube K be a field extension of degree 2, and prove that $$K \cong \mathbb{C}$$. Prove that there is no field extension $$\mathbb{R}$$ sube K of degree 3.

Mylo O'Moore 2021-02-02 Answered

### Let $$\displaystyle{G}={S}_{{3}}{\quad\text{and}\quad}{H}={\left\lbrace{\left({1}\right)}{\left({2}\right)}{\left({3}\right)},{\left({12}\right)}{\left({3}\right)}\right\rbrace}$$. Find the left cosets of $$\displaystyle{H}\in{G}$$.

Aneeka Hunt 2021-01-31 Answered

### Suppose G is a group and H is a normal subgroup of G. Prove or disprove ass appropirate. If G is cyclic, then $$\displaystyle\frac{{G}}{{H}}$$ is cyclic. Definition: A subgroup H of a group is said to be a normal subgroup of G it for all $$\displaystyle{a}\in{G}$$, aH = Ha Definition: Suppose G is group, and H a normal subgruop og G. THe froup consisting of the set $$\displaystyle\frac{{G}}{{H}}$$ with operation defined by (aH)(bH)-(ab)H is called the quotient of G by H.

Cem Hayes 2021-01-23 Answered

### Find the inverse of $$\displaystyle{x}+{1}\in\mathbb{Q}\frac{{{x}}}{{{x}^{{3}}-{2}}}$$. Explain why this is the same as finding the inverse of $$\displaystyle{\sqrt[{{3}}]{{{2}}}}\in\mathbb{R}$$.

Lewis Harvey 2021-01-06 Answered

### Prove that a group of even order must have an element of order 2.

Joni Kenny 2021-01-05 Answered

### Let a,b be coprime integers. Prove that every integer $$x>ab-a-b$$ can be written as $$na+mb$$ where n,m are non negative integers. Prove that $$ab-a-b$$ cannot be expressed in this form.

Dolly Robinson 2021-01-04 Answered

### Use Principle of MI to verify (i) If $$\displaystyle{n}\in\mathbb{Z}$$ is a positive ineger then $$\displaystyle{2}^{{n}}{3}^{{{x}{n}}}-{1}$$ divisible by 17. (ii) For all positive integers $$\displaystyle{n}\ge{5}$$, $$\displaystyle{2}^{{k}}{>}{k}^{{2}}$$

Harlen Pritchard 2020-12-15 Answered