Question

Give an example of abelian group consisting of 8 elements

Answer 1

Answer:

For another example, every abelian group of order 8 is isomorphic to either Z8 (the integers 0 to 7 under addition modulo 8), Z4 ⊕ Z2 (the odd integers 1 to 15 under multiplication modulo 16), or Z2 ⊕ Z2 ⊕ Z2..................................

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Answer 2

The example of abelian group consisting of 8 elements are listed below.

• Z8, Z4 Z2, and Z2 Z2 Z2 are the abelian groups of order 8 (up to isomorphism).
• Z4 Z2 is the only group with an element of order 4 but not 8, while Z8 is the only group with an element of order 8 as seen in .
• The only group on the list that has every non-zero element of order 2 is Z2 Z2 Z2.
• When two group elements are subjected to a group operation, the outcome is independent of the order in which the components are written.
• This is known as an abelian group, also known as a commutative group.
• The group operation is commutative, in other words.
• To demonstrate the set of integers Since I is an Abelian group, we must ensure that it satisfies the following five properties: closure, associativity, identity, inverse, and commutativity.
• Because of this, Closure Property is satisfied. Also met is the identity property.

The example of abelian group consisting of 8 elements are listed above.

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