Proof of Abelian Property of G Showing

Thread starter Punkyc7
Start date Jan 14, 2012

In summary, the Abelian property, also known as the commutative property, is a characteristic of a mathematical group where the order of multiplication does not affect the result. It is proven through various methods, such as using the group's defining operation or through induction. This property is important as it allows for more familiar and convenient algebraic operations to be used when working with the group. It is also a defining characteristic of a commutative group, meaning that a group cannot have the Abelian property without being commutative.

Jan 14, 2012

Punkyc7

Thanks I figured it out.

Last edited: Jan 15, 2012

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Jan 14, 2012

Poopsilon

Start with the identity (gh)^5 = g^5h^5, do what you can with inverses, then go to (gh)^3 = g^3h^3 and do the same, then see if you can make a substitution back into the first one, from here just see what's equal to what and play around for a bit with inverses, I didn't even need to use (gh)^4 = g^4h^4.

FAQ: Proof of Abelian Property of G Showing

What is the Abelian property of a group?

The Abelian property, also known as the commutative property, is a property of a mathematical group where the order in which elements are multiplied does not affect the result. In other words, for any two elements a and b in the group, a*b=b*a.

What does "proof of Abelian property of G showing" mean?

This phrase refers to a mathematical proof that demonstrates that a group G has the Abelian property. In other words, the proof shows that the group is commutative.

What is the importance of proving the Abelian property of a group?

Proving the Abelian property of a group is important because it allows us to use more familiar and convenient algebraic operations, such as addition or multiplication, when working with the group. This makes it easier to solve problems and make connections between different groups.

How is the Abelian property of a group proven?

The Abelian property is proven by showing that for any two elements a and b in the group, a*b=b*a. This can be done through various methods, such as using the group's defining operation or through induction.

Can a group have the Abelian property without being commutative?

No, a group cannot have the Abelian property without being commutative. The Abelian property is a defining characteristic of a commutative group, so if a group does not have this property, it is not considered commutative.