[代數] 幾題代數
1.Compute the indicated quantities for the given homomorphism ∮
Ker(∮)and∮(20) for ∮:Z→Z10 such that ∮(1)=6
2.Let G be any group and let "a" be any element of G.
Let∮:Z→G be defined by ∮(n)=a^n
Describe the image and the possibilities for the kernal of ∮.
3.Let G and G' be groups,and let H and H' be normal subgroups of G and G'
respectively.Let ∮ be a homomorphism of G into G'.
Show that ∮ induces a natural homomorphism ∮*:(G/H)→(G'/H') if ∮[H]屬於H'
4.Classify the given group according to the fundmental theorem of finitely
generated abelian group.
(Z4*Z8)/(<1,2>)
5.Show that if H is a subgroup of index 2 in a finite group G,then every
left coset of His also a right coset of H.
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