A finite group G with identity element e is said to be simple if {e} and G are the only normal subgroups of G, that is, G has no nontrivial proper normal subgroups. identity property for addition. c. (iii) Identity: There exists an identity element e G such that Identity element. Statement: - For each element a in a group G, there is a unique element b in G such that ab= ba=e (uniqueness if inverses) Proof: - let b and c are both inverses of a a∈ G . Then prove that G is an abelian group. Assume now that G has an element a 6= e. We will fix such an element a in the rest of the argument. If possible there exist two identity elements e and e’ in a group
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