GATE MA concept:cyclic-groups PYQs & Answers

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concept:cyclic-groups

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Questions 1–4 of 4. Imported answers require independent review unless marked reviewed.

Topic practice 4 questionsPage 1 of 1

Let

be the group of integers modulo

. Let

be the external direct product of

and

. Then which of the following statements is/are TRUE?

Your answerSelect all correct options. You can choose more than one.

is not a cyclic group.

The order of the element

is 98.

The order of the element

is 60.

There is an element in

of order 360.

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The number of subgroups of a cyclic group of order

is ________.

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Let

be a non-cyclic group of order 57. Then the number of elements of order 3 in

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Consider the following statements:

I. If

denotes the additive group of rational numbers and

is a non-trivial homomorphism, then

is an isomorphism.

II. Any quotient group of a cyclic group is cyclic.

III. If every subgroup of a group

is a normal subgroup, then

is abelian.

IV. Every group of order 33 is cyclic.

Which of the above statements are TRUE?

Your answerChoose one option.

II and IV only

II and III only

I, II and IV only

I, III and IV only

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GATE MA concept:cyclic-groups PYQs

How to practice concept:cyclic-groups

Question 54

Question 27

Question 52

Question 32