What Are the Elements of (Z4×Z12)/<2,1>?

In summary, Z4xZ12/<2,1>: Elements List is a mathematical concept that represents the set of all elements that can be obtained by multiplying an element from Z4 with an element from Z12 and then dividing by 2 and 1. To calculate the elements in Z4xZ12/<2,1>: Elements List, you need to list out all elements in Z4 and Z12, multiply them, and then divide by 2 and 1. The cardinality of Z4xZ12/<2,1>: Elements List is 24 and it is related to abstract algebra concepts and operations such as multiplication and division. Real-world applications of Z4xZ12/<2,1>: Elements List
  • #1
angubk6
2
0
List all elements of \[ (Z_4\times Z_{12})/<2,1> \]
 
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  • #2
Do you know what $Z_4$, $Z_{12}$ and <2,1> mean?
 

Related to What Are the Elements of (Z4×Z12)/<2,1>?

1. What is Z4xZ12/<2,1>: Elements List?

Z4xZ12/<2,1>: Elements List is a mathematical notation that represents the set of all elements in the group Z4xZ12 that are divisible by both 2 and 1.

2. How do you list the elements in Z4xZ12/<2,1>: Elements List?

To list the elements in Z4xZ12/<2,1>: Elements List, you would first list all the elements in the group Z4xZ12, which is the Cartesian product of Z4 and Z12. Then, you would take out any elements that are not divisible by both 2 and 1, leaving only the elements in Z4xZ12/<2,1>: Elements List.

3. What is the cardinality of Z4xZ12/<2,1>: Elements List?

The cardinality, or number of elements, in Z4xZ12/<2,1>: Elements List is equal to the number of elements in the group Z4xZ12 that are divisible by both 2 and 1. This can be calculated by taking the cardinality of Z4xZ12, which is 48, and dividing it by the number of elements that are not divisible by both 2 and 1, which is 2. Therefore, the cardinality of Z4xZ12/<2,1>: Elements List is 24.

4. How is Z4xZ12/<2,1>: Elements List used in mathematics?

Z4xZ12/<2,1>: Elements List is used in mathematics to represent a subset of elements in the group Z4xZ12 that satisfy a specific condition, in this case being divisible by both 2 and 1. It can also be used in group theory to study the properties and relationships between elements in this particular subgroup.

5. What is the significance of the notation Z4xZ12/<2,1>: Elements List?

The notation Z4xZ12/<2,1>: Elements List is significant because it allows us to easily identify and work with a specific subset of elements in the larger group Z4xZ12. It also highlights the use of modular arithmetic, as we are dividing the group by a specific element to create a new subgroup. This notation is commonly used in abstract algebra and group theory to represent different subgroups and their properties.

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