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of order n.50. Prove or disprove that H = {nEZIn is divisible by both 8 and 10)is a subgroup of Z.51. Suppose that G is a finite group with the property that every non-

Question

50

of order n.
50. Prove or disprove that H = {nEZIn is divisible by both 8 and 10)
is a subgroup of Z.
51. Suppose that G is a finite group with the property that every non-
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of order n. 50. Prove or disprove that H = {nEZIn is divisible by both 8 and 10) is a subgroup of Z. 51. Suppose that G is a finite group with the property that every non-

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Step 1

From the given information, it is needed to prove or disprove that H is a subgroup of Z:

H {ne Zn is divisible by both 8 and 10}
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H {ne Zn is divisible by both 8 and 10}

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Step 2

A number n € Z is divisible by both 8 and 10 if and only if it is divisible by lcm (8,10) = 40 that is:

n and 10n} =< 40 >is a subgroup of Z
{neZ8
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n and 10n} =< 40 >is a subgroup of Z {neZ8

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Step 3

Now, to prove that <40> is a subgroup of Z.

To show it is a ...

a,be H then ab
eH then H is a subgroup of G
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a,be H then ab eH then H is a subgroup of G

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