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- A group is a set with an operation that satisfies the following properties12:
- Closure: If ‘x’ and ‘y’ are two elements in a group, G, then x*y will also belong to G.
- Associativity: If ‘x’, ‘y’ and ‘z’ are in group G, then x*(yz) = (xy)*z.
- Identity: There exists an element ‘e’ in G, such that xe = ex = x for any ‘x’ in G.
- Invertibility: For every ‘x’ in G, there exists some ‘y’ in G, such that xy = yx = e.
Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.Group Theory Properties
- Closure: If ‘x’ and ‘y’ are two elements in a group, G, then x.y will also come into G.
- Associativity: If ‘x’, ‘y’ and ‘z’ are in group G, then x . (y . z) = (x . y) . z.
byjus.com/maths/group-theory/A group is a set G, combined with an operation *, such that:
- The group contains an identity
- The group contains inverses
- The operation is associative
- The group is closed under the operation.
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