Definition of a Group
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 Group
- Order of group G, o(G), is the number of distinct elements in G
a*b is in G if a, b are in Group G
(a*b)*c = a*(b*c)
if a, b, c are in Group G
1. Group G has an identity eG.
2. eG*c = c*eG = c if c is in Group G
1. if c is in G, c-1 is in G.
2. c*c-1 = c-1*c = eG
- ↑ Binary operation at wikipedia