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

frame| Identity: 1. Group G has an identity eG. 2. eG*c = c*eG = c if c is in Group G Let G be a group with binary operation Usages Usage1The identity of G, eG, is in group G. Usage2Group G has an identity eG Usage3If g is in G, eG g = g eG = g Usage4e is the identity of group G if e is in group G, and e g = g e = g for every element g in G. Notice 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