Abstract Algebra/Group Theory/Group/Definition of a Group/Definition of Identity
< Abstract Algebra | Group Theory | Group | Definition of a Group(Redirected from Abstract Algebra/Groups/Definition of a Group/Definition of Identity)
Let G be a group with binary operation
- The identity of G, eG, is in group G.
- Group G has an identity eG
- If g is in G, eG g = g eG = g
- e is the identity of group G if
- e is in group G, and
- e g = g e = g for every element g in G.
- eG always mean identity of group G throughout this section.
- G has to be a group
- If a is not in group G, a eG may not equal to a
- If is not the binary operation of G, a eG may not equal to a