# Abstract Algebra/Group Theory/Group/Definition of a Group

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< Abstract Algebra | Group Theory | Group

# Definition of a Group[edit]

Firstly, a Group is

- a non-empty set, with a binary operation.
^{[1]}

Secondly, if G is a Group, and the binary operation of Group G is , then

- 1. Closure
- 2. Associativity
- 3. Identity
- 4. Inverse

From now on, *e*_{G} always means identity of group G.

# Order of a Group[edit]

- Order of group G, o(G), is the number of distinct elements in G