Question: Let ( G, ) be a group. Consider the binary operation * on the set G defined by for a, b G. Show that

Let ( G, •) be a group. Consider the binary operation * on the set G defined by

a*b = b.a Dfor a, b ∈ G. Show that ( G, *) is a group and that ( G, *) is actually isomorphic to ( G, •). 

a*b = b.a D

Step by Step Solution

★★★★★

3.40 Rating (172 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

It is easy to see that G is a group because the order of multiplication in G is simply revers... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related A First Course In Abstract Algebra Questions!

Q:

Let G be a group where a2 = e for all a G. Prove that G is abelian.

Q:

Let G be a loop-free undirected graph, where = maxuV{deg(v)}. (a) Prove that x(G) + 1. (b) Find two types of graphs G, where x (G) = + 1.

Q:

Let G be a connected graph. Show that if T is a spanning tree of G constructed using depth-first search, then an edge of G not in T must be a back edge, that is, it must connect a vertex to one of...

Q:

plzzz i needed Q2,3 2. (a) Let S = {a,b,c}. How many closed binary operations * on S are there that satisfy the condition that for all x S we have r * x + x ? [2 marks] (b) Let S be a set of n > 2...

Q:

Need Handwritten solution with proper explanation as soon as possible 2. (a) Let G = {0. 1, ..., 2019}. Define a binary operation * on G by a+b if a + b 2020 (i) Show that . is associative, so G is a...

Q:

Let's determine most of the groups with 8 elements. Notice that Lagrange's theorem says that if g G and G has order 8, then o(g) = 1, 2, 4 or 8. (a) Let G be a group with an element of order 8. State...

Q:

please explain me!! Let G be a group. Consider the set Aut(G):= {f : G - GJf is an isomorphism } . Elements of Aut(G) are just isomorphisms from G to itself and are usually called automorphisms of G....

Q:

HW 12, MAT 312/AMS 351: SPRING 2017 Problem 1. (1) Set H = {4a + 6b | a, b Z} Z. Show that H is a subgroup of Z. (2) Is H cyclic? Problem 2. Write down all the cyclic subgroups of the following...

Q:

This Journal entry has two parts: Part A: Select TWO examples of solutions to trig identities from the Content section ( Examples or Check your Understanding ) or from Assignment 1 Solutions....

Q:

Isomorphiam refers to a precise type of structural equivalence between two groups (or between a group and itself). The idea is easy, but the formal definition may seem a bit tricky at first. A good...

Q:

The p.d.f. is h(t) = 1/t for 1 t e. Find the probability that the measurement is between 2.0 and 2.5. Find the probability in two ways: a. By integrating the given p.d.f. b. By using the c.d.f....

Q:

List the four types of responsibility centers and briefly describe each.

Q:

Question 3 9 1 pts Whereas Broca's area is involved in language q , , Wernicke's area is involved in language q , comprehension, production production, comprehension syntax, grammar grammar, syntax

Q:

When is the best time to practice psychological skills?

Q:

Using the information in the source table provided here, compute R 2 values for each effect. Using Cohens conventions, explain what these values mean. SS df MS Source A (rows) 30.006 30.006 0.511 B...

Q:

A researcher wondered about the degree to which age was a factor for those posting personal ads on Match.com. He randomly selected 200 ads and examined data about the posters (the people who posted...

Q:

In a study of racism, Nail, Harton, and Decker (2003) had participants read a scenario in which a police officer assaulted a motorist. Half the participants read about an African American officer who...

Q:

Twin sons, born in 1955, ended up life quite differently. One (Frank) retired at age 55 after the loss of his spouse to cancer Frank and his spouse never had children, and Frank was no longer...

Q:

24. You have saved $4,000 for a down payment on a new car. The largest monthly payment you can affort is $350. The loan will have a 12% APR based on end-of-month payments. What is the most expensive...

Q:

Suppose your current annual income is $120, 000 and you are planning on saving for living after retirement (in 40 years). You need $80, 000 every year after your retirement to maintain your living...