G is a group and H is a normal subgroup of G. List the elements of...

G is a group and H is a normal subgroup of G. List the elements of G/H and then write the table of G/H.

1. G=Z10, H= {0,5}. (Explain why G/H is congruent to Z5)

2. G=S4 and H= {e, (12)(34), (13)(24), (14)(23)

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Colby Messinger answered 2 weeks ago

Let G be a group and K ⊂ G be a normal subgroup. Let H ⊂...

Let G be a group and K ⊂ G be a normal subgroup. Let H ⊂ G be a subgroup of G such that K ⊂ H Suppose that H is also a normal subgroup of G. (a) Show that H/K ⊂ G/K is a normal subgroup. (b) Show that G/H is isomorphic to (G/K)/(H/K).

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Prove that a subgroup H of a group G is normal if and only if gHg−1 =H for all g∈G

Consider the subgroup H={R0,R180} of D6. List the elements of the factor group D6/H.

Let G be a finite group and H a subgroup of G. Let a be an...

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1. Let N be a normal subgroup of G and let H be any subgroup of...

1. Let N be a normal subgroup of G and let H be any subgroup of G. Let HN = {hn|h ∈ H,n ∈ N}. Show that HN is a subgroup of G, and is the smallest subgroup containing both N and H.

4.- Show the solution: a.- Let G be a group, H a subgroup of G and...

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Given a group G with a subgroup H, define a binary relation on G by a...

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G is a group and H is a normal subgroup of G. List the elements of...

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