Abstract Algebra/Group Theory/Group/Definition of a Group
< Abstract Algebra | Group Theory | Group
Definition of a GroupEdit
Firstly, a Group is
- a non-empty set, with a binary operation.
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, eG always means identity of group G.
Order of a GroupEdit
- Order of group G, o(G), is the number of distinct elements in G