Number of elements of order 6 in U(13)

#numberofelements #csirnet #shorttricks #grouptheory #abstractalgebra #modernalgebra

[@Zainabdullahoficial]

Does it hold for Z(10) also?? Like for all cyclic groups?

[@Menofmathematics123]

What when if it is not cyclic like number of elements of order 12 in U (90).

[@zubairsmathtutorials4542]

There are 4 elements of order 12 in U(90)

[@AdityaPandey-yl2ui]

​@@zubairsmathtutorials4542 Bro please check your answer ----- Phi(12) = 4 so number of elements of order 12 in U(90) is 4

[@speakingsarcasm9014]

U(90) is isomorphic to U(2)×U(3²)×U(5) which in turn is isomorphic to C_6 × C_4. In order to obtain an element of order 12 in this group, you need a pair (a,b) with order of a equal to 6 or 3 and order of b equal to 4. So answer is (2+2)×2 = 8.

[@speakingsarcasm9014]

​@@AdityaPandey-yl2uino that's wrong. U(90) is not cyclic. The trick shown in the video only works for cyclic groups.