abstract algebra, Mathematics

Assignment Help:
Let D(subscript12) = ({x,y : x^2 = e ; y^6 = e ; xy =(y^-1) x})
a) Which of the following subsets are subgroups of D(subscript12) ? Justify your answer.
i) {x,y,xy,y^2,y^3,e} ii) {xy,xy^2,y^2,e} iii) {x,y^3,xy^3,e}
b) Find the order of y^2. Is the subgroup (y^2) normal ? Justify your answer.
c) Let D(subscript2n) = ({x,y : x^2 = e ; y^n = e ; xy =(y^-1) x})
Prove the relation
{ x^i*y^(j+l) if k is even
X^i*y^j*x^k*y^l = {
{ x^(i+k)*y^(l-j) if k is odd
Further, find all the elements of order 2 in D(subscript12) .
D) Find two different Sylow 2-subgroups of D(subscript12) .

Related Discussions:- abstract algebra

Computing limits , Computing Limits :In the earlier section we saw that t...

Computing Limits :In the earlier section we saw that there is a large class of function which allows us to use to calculate limits. However, there are also several limits for whi

Calculus level 2, the first question should be done using the website given...

the first question should be done using the website given (www.desmos.com/calculator )and another good example to explain using the graph ( https://www.desmos.com/calculator/ydimzr

Example of factor by grouping, Factor by grouping each of the following. ...

Factor by grouping each of the following. 3x 2 - 2x + 12x - 8 Solution           3x 2 - 2x + 12x - 8 In this case we collect the first two terms & the final two te

Bussiness, How do these websites help the company strengthen its relationsh...

How do these websites help the company strengthen its relationships with its stakeholders? List the website(s) that you previewed and give examples to support your answers. Who are

Standard deviation, 2.When investigating times required for drive-through s...

2.When investigating times required for drive-through service, the following results (in seconds) were obtained. Find the range, variance, and standard deviation for each of the tw

Vectors, A triangle has vertices A (-1, 3, 4) B (3, -1, 1) and C (5, 1, 1)....

A triangle has vertices A (-1, 3, 4) B (3, -1, 1) and C (5, 1, 1). The area of ABC is a) 30.1 b) 82.1 c) 9.1 d) 52.1

Permatuation and combination problem, 4 boys and 4 girls are to seated in a...

4 boys and 4 girls are to seated in arow i)no. of girls sit together ii)not all girls sit together iii)boys and girls are altenate to each other iv)if a particular boy and g

Non linear relationships, Non Linear Relationships If the correlation ...

Non Linear Relationships If the correlation coefficient and the scatter diagram do not indicate linear relationship, then the relationship may be nonlinear. Two such relations

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd