Index of subgroup and coset of subgroup

Reference no: EM13125030

Explain what the index of a subgroup and a coset of a group are. Also, prove that if N is a subgroup of a group G such that [G: N] = 2, and if "a" and "b" are elements of G, then the product "ab" is an element of N if and only if either (1) both "a" and "b" are elements of N or (2) neither "a" nor "b" is an element of N.

Reference no: EM13125030

Questions Cloud

Determine the tax character of a recognized gain or loss : How do you determine the tax character of a recognized gain or loss? Would you rather have a realized gain or loss or a recognized gain or loss?

Identity elements of prime order : Suppose G is a finite group with the property that every non-identity element has prime order (D3 and D5 are examples of groups with this property).

Illustrate what is the overall impact on net income : Illustrate what is the overall impact on net income over the two accounting periods? (Negative amounts should be indicated by a minus sign. Omit the "$" sign in your response.)

Computing delta h : Calculating Delta H, Use some or all of the following reaction enthalpies to calculate delta H for the reaction:

Index of subgroup and coset of subgroup : Explain what the index of a subgroup and a coset of a group are. Also, prove that if N is a subgroup of a group G such that [G: N] = 2, and if "a" and "b" are elements of G,

Briefly discuss the major benefits of nafta : Discuss and explain the major provisions of the North American Free trade Area (NAFTA) agreement. Briefly discuss the major benefits of NAFTA to the U.S. economy.

Estimating the stocks price per share : The company has 10 million shares of stock outstanding. What is the best estimate of the stock's price per share?

Find the lowest income among the richest persons : Normally distributed with mean equal to 15,000 and standard deviation equal to 1000. What is the lowest income among the richest 250 persons?

What is the amount of the loss on impairment : What is the amount of the loss on impairment that Beehive should recognize at June 30, 2006?

User Account

All Pages