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

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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


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  1. The identity of G, eG, is in group G.
  2. Group G has an identity eG
  3. If g is in G, eG g = g eG = g
  4. 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.


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  1. eG always mean identity of group G throughout this section.
  2. G has to be a group
  3. If a is not in group G, a eG may not equal to a
  4. If is not the binary operation of G, a eG may not equal to a