Theorem 6.23: Let o be a homomorphism function from group G to group G. Then following results hold. ◆(1)Kerφ;] is a normal subgroup of[G; . (2)p is one-to-one iff K=(ed) ◆(3)|p(G;] is a subgroup of g';°l proof:(1)i Kero is a subgroup of g ◆ For va,b∈kerq,a2b∈?kerq, ◆ie.g(a2b)=?ec ◆ Inverse element: For va∈Kerq,al∈?Kerp ◆i) For GeC,2a∈Kerq,g1*a*g∈?Kerq Theorem 6.23：Let  be a homomorphism function from group G to group G'. Then following results hold.  (1)[Ker;*] is a normal subgroup of [G;*].  (2) is one-to-one iff K={eG}  (3)[(G); •] is a subgroup of [G';•].  proof:(1)i) Ker is a subgroup of G  For a,bKer, a*b?Ker,  i.e.(a*b)=?eG‘  Inverse element: For aKer, a -1?Ker  ii)For gG,aKer, g-1*a*g?Ker