GATE MA concept:normal-subgroups PYQs & Answers

Questions 1–3 of 3. Imported answers require independent review unless marked reviewed.

Let

be a group of order 595. Which one of the following is TRUE?

Your answerChoose one option.

cannot have a proper normal subgroup.

must have a proper normal subgroup.

cannot have an element of order 17.

The number of Sylow 5-subgroups is 17.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

Which one of the following statements is true?

Your answerChoose one option.

Every group of order 12 has a non-trivial proper normal subgroup

Some group of order 12 does not have a non-trivial proper normal subgroup

Every group of order 12 has a subgroup of order 6

Every group of order 12 has an element of order 12

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

GATE MA concept:normal-subgroups PYQs