direct product of groups number of elements of order n in Zn Z15xZ5 direct product in group theory

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Massachusetts Institute of Technology (MIT), United States, Harvard University, Stanford University, University of Cambridge, United Kingdom, University of Oxford, University of California, Berkeley (UCB), Princeton University, ETH Zurich (Swiss Federal Institute of Technology), Switzerland, University of California, Los Angeles (UCLA), New York University (NYU)
Group Theory: Groups, subgroups, Abelian groups, non-Abelian groups, cyclic groups, permutation groups, normal subgroups, Lagrange's Theorem for finite groups, group homomorphism, and basic concepts of quotient groups.
direct product the number of elements of order n in Zn is phi(n) Z15xZ5 group theory BHU PET 2019
tag 23072021
19. The number of elements of order 5 in the group Z_15×Z_5 is
(a) 16 (b) 24 (c) 8 (d) 4
En BHU PET 2019, 19
Key (b)

[@sanjana5866]

amazing video......"if d is a poisitive divisors of n ,then the no of elements of order d in cyclic group of order n is phi(d)" this theorem is applicable on Z because it is cyclic then in case of U,S6 it wiil apply???

[@sreesaivjm8750]

Also (1,5) is not an element in this group, is it?

[@little_bit_curious5122]

Thank you sir

[@SantoshiFamily]

You're welcome

[@sivaram8033]

Sir ans a mark pannunga plz

[@sreesaivjm8750]

How(5,5) is possible

[@samuelsabeng8930]

What will fhi(9) be sir, want to know.

[@SantoshiFamily]

6

[@user-wh7xl5uz8e]

3² -3¹ =6

[@subhadipsarkar7692]

♥️

[@SantoshiFamily]

Thanks for like our video

[@himanshunegi9384]

Yha kha kmm ata hi

[@jagadeesma9738]

How to find pi(d)=4

[@SantoshiFamily]

Absolutely right

[@abhishekrawat6914]

Sir ye jo 1000 groups ke mcq hai kya ye csir net ke liye enough hai

[@SantoshiFamily]

Yes

[@samuelsabeng8930]

Good sir but am still having troubles how fhi(5)=4

[@SantoshiFamily]

There is a formula to find phi(n),

[@user-wh7xl5uz8e]

5¹ -1

[@tanmoypaul393]

thanks sir

[@SantoshiFamily]

Most welcome

[@Rathan13784]

B is the ans

[@SantoshiFamily]

Thanks for your feedback

[@sakshipandey2031]

Samjh nhi aaya

[@windsofvalley]

Mara bii yahi haal... Bakwaas bol raha ha

[@itsdarksoul8778]

Bhai Hindi bol k steps b clearly samjha ta toh achha hota

[@gaukiduniya3199]

Muze nhi lgta

[@SantoshiFamily]

Thanks for your feedback

[@nonsense3823]

So disgusting

[@SantoshiFamily]

Thanks for your feedback