Which of the following equations can occur as the class equation of a group of order 10?

This question was previously asked in
CSIR UGC (NET) Mathematical Science: Held On (7 June 2023)
View all CSIR NET Papers >
  1. 10 = 1 + 1 + … + 1 (10-times)
  2. 10 = 1 + 1 + 2 + 2 + 2 + 2
  3. 10 = 1 + 1 + 1 + 2 + 5
  4. 10 = 1 + 2 + 3 + 4

Answer (Detailed Solution Below)

Option 1 : 10 = 1 + 1 + … + 1 (10-times)
Free
Seating Arrangement
3.3 K Users
10 Questions 20 Marks 15 Mins

Detailed Solution

Download Solution PDF

Concept:

If G be a group such that o(G) = 2p where p is odd prime then G ≅ \(\mathbb Z_{2p}\) or G ≅ \(\mathbb D_p\)

(ii) If o(G) = n where G is abelian group then class equation of G is n = 1 + 1 + ... + 1 (n times)

Explanation:

Given o(G) = 10 = 2.5

So here p = 5 which is odd prime.

Hence G ≅ \(\mathbb Z_{10}\) or G ≅ \(\mathbb D_5\)

If G ≅ \(\mathbb Z_{10}\) then it is cyclic so abelian. Therefore class equation of a group of order 10 is 10 = 1 + 1 + … + 1 (10-times)

If G ≅ \(\mathbb D_5\) then there will be 5 rotation and 5 reflection.

So in this case class equation of a group of order 10 is 

10 = 1 + 2 + 2 + 5

Hence option (1) is correct

Latest CSIR NET Updates

Last updated on Jun 5, 2025

-> The NTA has released the CSIR NET 2025 Notification for the June session.

-> The CSIR NET Application Form 2025 can be submitted online by 23rd June 2025

-> The CSIR UGC NET is conducted in five subjects -Chemical Sciences, Earth Sciences, Life Sciences, Mathematical Sciences, and Physical Sciences. 

-> Postgraduates in the relevant streams can apply for this exam.

-> Candidates must download and practice questions from the CSIR NET Previous year papers. Attempting the CSIR NET mock tests are also very helpful in preparation.

Get Free Access Now
Hot Links: teen patti master downloadable content teen patti casino apk teen patti vip teen patti bonus