(a) Suppose K is a subgroup of H, and H is a subgroup of G. If...

(a) Suppose K is a subgroup of H, and H is a subgroup of G.
If |K|= 20 and |G| = 600, what are the possible values for |H|?
(b) Determine the number of elements of order 15 in Z30 Z24.

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Colby Messinger answered 2 years 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).

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

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

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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.

Let G, H, K be groups. Prove that if G ≅ H and H ≅ K...

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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...

Given a group G with a subgroup H, define a binary relation on G by a ∼ b if and only if ba^(-1)∈ H. (a) (5 points) Prove that ∼ is an equivalence relation. (b) (5 points) For each a ∈ G denote by [a] the equivalence class of a and prove that [a] = Ha = {ha | h ∈ H}. A set of the form Ha, for some a ∈ G, is called a right coset of H...

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(a) Suppose K is a subgroup of H, and H is a subgroup of G. If...

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