Advanced Algebra (lecture 4.C)|Show that every homomorphic image of solvable group G is solvable.

title: Advanced Algebra (lecture 4.C)| Solvable groups| Let G be a solvable group. Show that every homomorphic image of G is also solvable

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Links of previous lectures:

lecture 1:    • Advanced Algebra (lecture 1)| Series ...  
lecture 2:    • Advanced Algebra (lecture 2)| Jordan ...  
lecture 3:    • Advanced Algebra (lecture 3)|  Schrei...  
lecture 4.A:    • Advanced Algebra (lecture 4.A)| Solva...  
lecture 4.B:    • Advanced algebra (lecture 4.B)| Every...  

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Show that every homomorphic image of solvable group G is solvable
solvable group
abstract algebra
solvable groups
every abelian group is solvable
solvable series
homomorphic image of solvable group
advanced abstract algebra
group of quaternions
examples of solvable group

Thank you