Question: Suppose G is a group with n elements, and H is a subgroup of G with M elements. A.) Suppose H not equal to G

Suppose G is a group with n elements, and H is a subgroup of G with M elements.

A.) Suppose H not equal to G and gH in G-H. Let gH={gh:H in H}.

Show that the intersection of H and gH is the nulls so that the order of the Union of H and gH=2m


Step by Step Solution

★★★★★

3.40 Rating (178 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock 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 Accounting Questions!

Q:

Let G be a simple graph. Show that the relation R on the set of vertices of G such that uRv if and only if there is an edge associated to {u, v} is a symmetric, ir-reflexive relation on G.

Q:

Let X1,..., Xn be iid Poisson(). Show that the family of distributions of Xi is complete. Prove completeness without using Theorem 6.2.25.

Q:

Let X1,..., Xn be iid Bernoulli(p). Show that the variance of attains the Cramer-Rao Lower Bound, and hence is the best unbiased estimator of p.

Q:

18. 19. 20. 21. 22. 23. 24. 25 26 27 29. 30. 31. 32. 33. 34. 35. Suppose that a is a group element and a6 E e. What are the possi- bilities for lal? Provide reasons for your answer. If a is a group...

Q:

Show that if G is a finite group with identity e and with an even number of elements, then there is a e in G such that a * a = e.

Q:

Show that for n 3, there exists a nonabelian group with 2n elements that is generated by two elements of order 2.

Q:

Suppose that \(D^{(\alpha)}\) and \(D^{(\beta)}\) are irreps of a compact simple group with dimensions \(n_{\alpha}\) and \(n_{\beta}\), respectively, and basis vectors \(x_{i}\) and \(y_{i}\),...

Q:

Verify that the mapping \(e ightarrow 1\) and \(a ightarrow-1\) gives a representation of the cyclic group \(\mathrm{C}_{2}\) described in Box 2.2 that preserves the group multiplication, as does the...

Q:

3. Suppose that you observe that the wages for accountants in your town have gone up and that the number of accountants employed has also gone up. Whi one of the following conditions could explain...

Q:

1. 3. Suppose that you observe that the wages for accountants in your town have gone up and that the number of accountants employed has also gone up. Whi one of the following conditions could explain...

Q:

Refer to the Turner Hardware information in E12- 37B. Compute the ARR for the investment. In E12- 37B Turner Hardware is adding a new product line that will require an investment of $ 1,450,000....

Q:

4. The equilibrium constant for O2 = 20 is 2.4547 (102) atm. at 3100 K. What is the equilibrium constant for the O = O2 at the same temperature? Clearly show units for the answer.

Q:

Vacation pay on termination would be recorded in which Block ( s ) on the Record of Employment? Block 1 5 B only Block 1 7 A only Blocks 1 5 B . 1 5 C PP 1 and 1 7 A It would not be recorded

Q:

What are the six core ethical values described by the Josephson Institute? What are some other sources of ethical values?

Q:

Serial Bond Debt Service Fund Journal Entries and Financial Statements. As of December 31, 2010, New Town had $9,500,000 in 4.5 percent serial bonds outstanding. Cash of $509,000 is the debt service...

Q:

The current price of silver is $30 per ounce. The storage costs are $0.48 per ounce per year payable quarterly in advance. Assuming that interest rates are 10% per annum for all maturities, calculate...

Q:

Presented below is information related to Lexington Real Estate Agency. Oct. 1 Diane Lexington begins business as a real estate agent with a cash investment of $20,000 in exchange for common stock. 2...

Q:

Edgefield Corporation h as issued 10%, participating, and cumulative preferred stock with a total par value of $22,000 LO 16.1 and common stock with a total par value of $66,000. Therefore, the...

Q:

What's the best answer 01/15 You have to work outside on a ladder. The ground is uneven and the ladder isn't stable. How should your supervisor control this hazard? O Put boards underneath the ladder...

Q:

Here is a method for constructing a polynomial Q[x] with Galois group S n for a given n > 3. It depends on the fact that there exist irreducible polynomials of every degree in Z p [x] (p prime;...

Q:

In using the three isomorphism theorems, it is often necessary to know the actual correspondence given by the isomorphism and not just the fact that the groups are isomorphic. Repeat Exercise 3 for...

Q:

In using the three isomorphism theorems, it is often necessary to know the actual correspondence given by the isomorphism and not just the fact that the groups are isomorphic. In the group Z 24 , let...

Q:

Show how all possible G-sets, up to isomorphism (see Exercise 9), can be formed from the group G. Let X i for i I be G-sets for the same group G, and suppose the sets X i are not necessarily...

Q:

In using the three isomorphism theorems, it is often necessary to know the actual correspondence given by the isomorphism and not just the fact that the groups are isomorphic. In the group G = Z 24 ,...

Q:

Give a one-sentence synopsis of the proof of Theorem 10 .10. Data from Theorem 10.10 Let H be a subgroup of a finite group G. Then the order of H is a divisor of the order of G. Proof Let n be the...