subgroup and homomorphic image of a solvable group is solvable.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.6: Homomorphisms
Problem 20E: 20. If is an abelian group and the group is a homomorphic image of , prove that is abelian.
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Every subgroup and homomorphic image of a solvable group is solvable.

 

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