Conjugate subgroups homomorphisms and isomorphisms

Reference no: EM13124438

Direct Products of Groups, Conjugate Subgroups, Homomorphisms and Isomorphisms

Assume that K is a cyclic group, H is an arbitrary group and f1 and f2 are homomorphisms from K into Aut(H) such that f1(K) and f2(K) are conjugate subgroups of Aut(H). If K is infinite, assume f1 and f2 are injective. Prove by constructing an explicit isomorphism that (H x_f1 K) is isomorphic (H x_f2 K)

Reference no: EM13124438

Questions Cloud

What is the maximum possible yield of nh3 : If 101 g of CaO and 261 g of NH4Cl are mixed, what is the maximum possible yield of NH3?What mass of the excess reactant remains after the maximum amount of ammonia has been formed?

Finding value of system of equation : Find the value of x & y that solve the following system of equations:

Illustrate what is the income reported by dodge : During 2012 Gates reported net income of $200,000 and reported dividends of $75,000. Illustrate what is the income reported by Dodge for 2012 with regard to the Gates investment?

Which of the following statements is accurate : A tract of land was distributed by MNO Inc. to its sole shareholder, Martha, as a dividend. At the time of the distribution, MNO Inc.'s adjusted basis in the land was $40,000, the fair market value of the land was $80,000, and the land was encumbe..

Conjugate subgroups homomorphisms and isomorphisms : Direct Products of Groups, Conjugate Subgroups, Homomorphisms and Isomorphisms, Assume that K is a cyclic group, H is an arbitrary group and f1 and f2 are homomorphisms from K into Aut(H) such that f1(K) and f2(K) are conjugate subgroups of Aut(H)

Solving systems of equations : There are many applications used in the area of solving systems of equations. For example, systems of equations can be used to find the optimal number of items to produce to ensure the highest profit of those particular items.

Unhappy circumstances : Many people live within unhappy circumstances and yet will not take the initiative to change their situation because they are conditioned to a life of security, conformity, and conservatism, all of which may appear to give one peace of mind, but in r..

Calculate the ph of a solution : Calculate the pH of a solution formed by mixing 65-mL of 0.22M NaHCO3 with 75-mL of 0.15M Na2CO3.

Selling the assets and paying the liabilities : After selling the assets and paying the liabilities, the partnership has cash of $92,000. How much cash will each partner receive in the final liquidation?

User Account

All Pages