 # Abstract algebra questions and answers

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

### Prove that if "a" is the only elemnt of order 2 in a group, then "a" lies in the center of the group. vestirme4 2021-02-06 Answered

### What is Triangularization of linear operator BolkowN 2021-02-05 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

### Let $$\displaystyle{H}={\left\lbrace\sigma\in{S}_{{5}}{\mid}\sigma{94}\right)}={4}\rbrace$$ Show that $$\displaystyle{H}\le{S}_{{5}}$$ Clifland 2021-01-31 Answered

### In an abstract algebra equation about groups, is "taking the inverse of both sides of an equation" an acceptable operation? I know you can right/left multiply equations by elements of the group, but was wondering if one can just take the inverse of both sides? foass77W 2021-01-27 Answered

### Let G be a group of order $$\displaystyle{p}^{{m}}$$ where p is prime number and m is a positive integer. Show that G contains an element of order p. nagasenaz 2021-01-25 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

### what is abelin group? arenceabigns 2021-01-19 Answered

### In group theory (abstract algebra), is there a special name given either to the group, or the elements themselves, if $$\displaystyle{x}^{{2}}={e}$$ for all x? necessaryh 2021-01-15 Answered

### In the froup $$\displaystyle{Z}_{{12}}$$, find |a|, |b|, and |a+b| a=6, b=2 foass77W 2021-01-08 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

### Let F be a field and consider the ring of polynominals in two variables over F,F[x,y]. Prove that the functions sending a polyomial f(x,y) to its degree in x, its degree in y, and its total degree (i.e, the highest $$i+j$$ where $$\displaystyle{x}^{{i}}{y}^{{i}}$$ appears with a nonzero coefficient) all fail o be norm making F[x,y] a Euclidean domain. texelaare 2020-12-30 Answered

### In the froup $$\displaystyle{Z}_{{12}}$$, find $$|a|, |b|$$, and $$|a+b|$$ $$a=3, b=8$$ hexacordoK 2020-12-27 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

### Suppose G is a group, H a subgroup of G, and a and b elements of G. If $$\displaystyle{a}\in{b}{H}$$ then $$\displaystyle{b}\in{a}{H}$$. nicekikah 2020-12-15 Answered

### How many subgroups of order 4 does $$\displaystyle{D}_{{4}}$$ have? Rui Baldwin 2020-12-15 Answered

### Let F be i field with subfields K,L. Prove that there is a largest subfield of F contained in both K and L, and a smallest subfield of containung both K and L.

Coming up with good abstract algebra examples is essential for those who are trying to come up with the answers to theoretical questions both in Engineering and Data Science disciplines. The college students will be able to discover abstract algebra questions and answers provided by our friendly experts that will help you to understand abstract algebra questions with various examples based on high-energy physics, cryptography, and the number theory. Remember that the trick is to use number sequences to generalize the set of various integers at play. Don’t forget about the application of the Algebraic number theory studies as well.
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