Determining nilpotent groups

Reference no: EM13125737

Let G = UT (n,F) be the set of the upper triangular n x n matrices with entries in a field F with p elements and 1's on the diagonal. The operation in G is matrix multiplication.

(a) Show that G is a group

(b) Show that G is a finite p-group

1 = Z_0 (G) <= Z_1 (G) <= Z_2 (G) <=....<= Z_c (G) = G

Write explicitly what Z_1 (G), Z_2 (G), and Z_3 (G) are.

Show that Z_3 / Z_2 = Z (G/Z_2)

Prove that G is nilpotent of class exactly n-1.

Reference no: EM13125737

Questions Cloud

Calculate the mean difference for the data : Calculate the mean difference for the following data. The scores are the number of pictures the participants remembered correctly out of 20.

What percentage time amount of rainfall in april exceeds : A month is classified as extremely wet if the amount of rainfall is in the upper 10% for that month. How much precipitation must fall before a month of April is classified as extremely wet?

Promoting the profession of accountancy : You have been elected president of your university's newly chartered accounting honor society. The society is a chapter of a national organization that has the following mission: "To promote the profession of accountancy as a career and to imbue m..

What is the percentage chlorine by mass in the organic : What is the percentage chlorine by mass in the organic compound?" and got an answer of 37.1% Cl, which im pretty sure is right.

Determining nilpotent groups : Let G = UT (n,F) be the set of the upper triangular n x n matrices with entries in a field F with p elements and 1's on the diagonal. The operation in G is matrix multiplication.

Which is approximate cash collections amount for qquarter : Assume Green Leaf Nursery anticipated sales of $500 in this quarter. Accounts receivable at the beginning of the quarter was $300. Assuming a collection period of 30 days, which is the approximate cash collections amount for the quarter?

Calculate the theoretical yield of c2h5cl : Calculate the theoretical yield of C2H5Cl when 135 g of C_2H_6 reacts with 225 g of Cl_2, assuming that C_2H_6 and Cl_2 react only to form C_2H_5Cl and HCl.

Determine probability that all had starting salary in range : Of the physics graduates at a university, 30% had a starting salary of $30,000 or more. If five of the graduates are selected at random, find the probability that all had a starting salary of $30,000 or more.

When making an alcoholic beverage : When making an alcoholic beverage, such as beer and wine, Brix is a measurement used to assess the amount of sugar present in the fermentation matrix or grape juice.

User Account

All Pages