###### GATE 2017 [Set-1]

October 14, 2023###### GATE 2007

October 14, 2023# GATE 2007

Question 21 |

How many different non-isomorphic Abelian groups of order 4 are there?

2 | |

3 | |

4 | |

5 |

Question 21 Explanation:

In this problem first of all we find the exponents of prime nos. that can be taken out from given number.

4 = 2

So, prime no. is 2 and power of 2 is 2. So exponent value 2 is considered now.

Now the no. of ways we can divide 2 into sets will be the answer.

So division can be done as,

{1,1}, {0,2}

in two ways. Hence, answer is 2.

4 = 2

^{2}So, prime no. is 2 and power of 2 is 2. So exponent value 2 is considered now.

Now the no. of ways we can divide 2 into sets will be the answer.

So division can be done as,

{1,1}, {0,2}

in two ways. Hence, answer is 2.

Correct Answer: A

Question 21 Explanation:

In this problem first of all we find the exponents of prime nos. that can be taken out from given number.

4 = 2

So, prime no. is 2 and power of 2 is 2. So exponent value 2 is considered now.

Now the no. of ways we can divide 2 into sets will be the answer.

So division can be done as,

{1,1}, {0,2}

in two ways. Hence, answer is 2.

4 = 2

^{2}So, prime no. is 2 and power of 2 is 2. So exponent value 2 is considered now.

Now the no. of ways we can divide 2 into sets will be the answer.

So division can be done as,

{1,1}, {0,2}

in two ways. Hence, answer is 2.

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