Question: If G is a group, let H = [a G|ag = ga for all g G}. Prove that H is a subgroup of

If G is a group, let H = [a ∈ G|ag = ga for all g ∈ G}. Prove that H is a subgroup of G. (The subgroup H is called the center of G.)

Step by Step Solution

★★★★★

3.41 Rating (170 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Since eg ge for all g G it follows that e H and H If x y H th... 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

Document Format (1 attachment)

Word file Icon

954-M-L-A-L-S (8517).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

If G is a group, prove that for all a, b G, (a) (a-1)-1 = a (b) (ab)-1 = b-1a-1

Q:

If G is a group of even order, prove that there is an element a G with a e and a = a-1.

Q:

Let f be integrable on [a, b] and E be a finite subset of [a, b]. Show that If g is a bounded function which satisfies g(x) = f (x) for all x [a, b]E, then g is integrable on [a, b] and gix) dx =...

Q:

Let G be a group and H a cyclic normal subgroup of G. Prove that every subgroup of H is a normal subgroup of G.

Q:

Math 3310 - Algebraic Structures I 12/12/11 Final Ir Give precise denitions 4 of the following 7. (5 points each) 1 2 3 4 5 6 7 II. Work 3 of the following 5 problems. Determine if the statement is...

Q:

Hi any help with these questions are greatly appreciated! 1) Let x, y, a, b be elements of a group G. (a) Show that x, x^(1), yxy^(1) all have the same order. (b) Using the fact that x and yxy^(1)...

Q:

9 . 9 = e. = 92 = e. 47. Let G be an abelian group. Let H be the subset of G consisting of the identity e together with all elements of G of order 2. Show that H is a subgroup of G. pf) Let G be an...

Q:

Solve action. 2. Let (F, +, .) be a field. Let G = (F, .) the group. Let V be any vector space over F (Refer chapter on Vector spaces). Define * by a * v = a.v, a e F, v E V, where . is scalar...

Q:

5. Let G be a group, let a be an element of G, and let N(a) = {g G | gag = a" and gag = a* for some n, k Z} . Prove that N(a) is a subgroup of G. (Suggestion: Note that (gag)(gag) = gag; you may find...

Q:

1. Mark each statement True or False: And explain your answer : (a) Let G be a group and H be a subgroup of G. Then H is a subgroup of its normalizer N(H). (b) The dihedral group D, can be expressed...

Q:

What mass of phosphorus is needed to dope l.0 g of silicon to the extent described in Sample Problem 41-6?

Q:

During the 2019-2020 ski season, a season pass for Ski Santa Fe cost $800 and gave the holder unlimited access from the start of the season on Thanksgiving Day to the end of the season, which was cut...

Q:

What are the characteristics of modern accounting ? State the advantages and limitations of accounting ?

Q:

Supremacy Clause. The Federal Communications Act of 1934 grants the right to govern all interstate telecommunications to the Federal Communications Commission (FCC) and the right to regulate all...

Q:

Evan is standing at one corner of the football field when he sees his dog, Spot, start to run diagonally across the field as shown. Evan knows that Spot can run to the opposite corner in 15 s. The...

Q:

D'Andre surveyed a randomly chosen group of 15 teachers at his school and asked them how many students were enrolled in their third-period classes. Here is the data set he collected. {27, 29, 18, 34,...

Q:

Rewrite each equation in standard form, and identify the type of curve. a. 25x2 - 4y2 + 100 = 0 b. 4y2 - 10x + 16y +36 = 0 c. 4x2 + 4y2 + 24x - 8y + 39 = 0 d. 3x2 + 5y2 - 12x + 20 y + 8 = 0

Q:

1.Ayn banda, sarf malzemeleri 5.500 dolard. Ay boyunca 6.000 $'lk sarf malzemesi satn alnd. Ay sonunda, 4.000 adet malzeme hl hazr durumda. Ayar girii nedir? Sarf Malzemeleri hesabndaki biti...

Q:

Use technology to compute the balance in each of the following accounts. a . An account with monthly compounding, an APR of 6 % , and an initial deposit of $ 1 0 0 0 , after 5 years b . An account...

Q:

A variety of interested parties-including existing and prospective creditors (such as lenders and suppliers), employees and managers, shareholders, regulators, security analysts, and...