For each group in the following list find the order of each element in the group:...

For each group in the following list find the order of each element in the group: Z₁₂, U(10) and U(12).

Expert Solution

Please find the solution.

Definition 1: For G an additive group and x?G define the order of x to be the smallest positive integer n such that n.x = Identity of the group, and denote this integer by O(x).

Definition 2: For G a multiplicative group and x?G define the order of x to be the smallest positive integer n such that x^n = Identity of the group, and denote this integer by O(x).

So we will use Definition 1 for Z(12) because Z(12) is an additive group under modulo 12 and '0' is its identity element and Definition 2 for U(10) & U(12) are multiplicative groups under modulo 10 and 12 respectively and '1' is its identity element

Please rate the solution> if you still have doubts about this solution, comment below. Thanking you

milcah answered 1 year ago

Find the order and the inverse of the element in the indicated group. (a) (17, 4)...

Find the order and the inverse of the element in the indicated group. (a) (17, 4) ∈ Z-18 × Z-18 (b) (10,(1 4 5),(1 2)(3 4 5)) ∈ Z-12 × A-5 × S-5 (c) (35, 18, 30, 4) ∈ Z-45 × Z-26 × Z-35 × Z-38

Write the multiplication table for D8. Find the order of each element D8.

Identify the element the fits each of the following descriptions a. most nonmetallic element in group...

Identify the element the fits each of the following descriptions a. most nonmetallic element in group VIA b. most metallic element in group IA c. most nonmetallic element in period 3 d. most metallic element in period 2

Let a be an element of a finite group G. The order of a is the...

Let a be an element of a finite group G. The order of a is the least power k such that ak = e. Find the orders of following elements in S5 a. (1 2 3 ) b. (1 3 2 4) c. (2 3) (1 4) d. (1 2) (3 5 4)

Let G be a group of order 40. Can G have an element of order 3?

Each of the following letters represents an unknown main group element. Your task is to use the clues provided to place them in their correct order on.

Each of the following letters represents an unknown main group element. Your task is to use the clues provided to place them in their correct order on. The unknown elements are clustered by group, but they are not in order:FYQ ZBI PVEJ ANU WDM COGT HLS RXKClues:C has the least number of protons in its groupThe atomic number of O is 3 times that of MB is the most electronegative element on the periodic tableG is a noble gasH is...

Prove that any non identity element of a free group is of infinite order

1.List the individual components of Generally Accepted Auditing Standarts, by group in order, briefly describing each,...

1.List the individual components of Generally Accepted Auditing Standarts, by group in order, briefly describing each, and indetify the widely used acronym to indetify each individually and all as a group. 2. List and briefly describe the four different types of auditors opinion reports that an auditor can render and include the simple practice aid tool, phrase, symbol or icon that is generally uses to quick reference indentify each. 3. List and briefly describe, measures yhat a cpa firm shoul...

Find the center of S3 and the centralizer of each element of S3

Let B be a finite commutative group without an element of order 2. Show the mapping...

Let B be a finite commutative group without an element of order 2. Show the mapping of b to b2 is an automorphism of B. However, if |B| = infinity, does it still need to be an automorphism?

Question