Let G and H be groups, and let N be a normal subgroup of G. Decide whether each of the following two statements is true or false. Give a proof or a counterexample in each case. (a) The group G × H is abelian if and only if G and H are both abelian. (b) The group G/N is abelian if and only if both G and N are abelian.
Let G and H be groups, and let N be a normal subgroup of G. Decide whether each of the following two statements is true or false. Give a proof or a counterexample in each case. (a) The group G × H is abelian if and only if G and H are both abelian. (b) The group G/N is abelian if and only if both G and N are abelian.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.3: Subgroups
Problem 6TFE: True or false
Label each of the following statements as either true or false, where is subgroup of...
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