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###### Mahima posted an Question
January 29, 2021 • 10:04 am 30 points
• IIT JAM
• Mathematics (MA)

## How many subgroups of order 5 are contained in z, x z,?

How many subgroups of order 5 are contained in Z, x Z,?

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• ##### Anonymous User Best Answer

Mahima see attachment

Its very useful

thank u dear

• ##### Anonymous User

See attachment below

PFA.

• ##### Piyush pachauri

Any doubt then you can ask

• ##### Piyush pachauri

It has 24 elements of order 5. So 6 subgroups of order5 . It is no of elements of order n divided by phi(n). 24/(5-1) =6

Sir i dont understand,how to calculate number of elements(24)

okay, Z5 has 4 elements of order 5 and 1 is identity. Now in Z5\u00D7Z5check for LCM(O(a),O(b)) =5 ,O(a) = order of a in first Z5 and order of b in second Z5 LCM(1,5) = 5 so 4 elements like (0,1),(0,2)etc LCM(5,1) = 5 so 4 elements like (1,0) ,(2,0)etc Lcm(5,5) = 5 so 16 elements like (1,1),(1,2) ... So total 4+4+16 = 24 elements