4*. Let f G H be a group homomorphism. Prove: (a) If S G then f(S) 4 f(G) (b) Show by example that S aG need not imply f(S) (c) If T H then f1(T) G. H
4*. Let f G H be a group homomorphism. Prove: (a) If S G then f(S) 4 f(G) (b) Show by example that S aG need not imply f(S) (c) If T H then f1(T) G. H
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter4: More On Groups
Section4.6: Quotient Groups
Problem 30E: Let G be a group with center Z(G)=C. Prove that if G/C is cyclic, then G is abelian.
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