proving question?

Question

Let G be a group of order ab where a and b are distinct primes. Prove that every proper subgroup of G is cyclic.

Answer 1

By Lagrange's theorem, the order of a subgroup H of G must be a factor of the order of G. So |H| divides ab. Since H is a proper subgroup, its order can't be ab. Since a and b are prime, this means that the order of H must be a, b, or 1. Any group of prime order is cyclic, and the trivial group is cyclic trivially. Cheers!

Answer 2

Although your question is of the Quernerzs kind, I will answer it. To find this answer, you would need only find the tanh of the 34 of cosine, and then add that number by the factor 45, then from this point you would need to figure out how much light the Focal Light Particle Compact Projector emits. Remember in space light is in a vacuum, your answer would not be the answer you receive once you found that out. Of course as light goes through the FLPCP time is warped, matter slows down, and begins to convert into high energy, so whatever particle is coming out, say light for example, you would then use advanced algorisms to calculate the speed light would take from the FLPCP to travel 234,567,876,987,456,678,345,678,345, gigalightyears, then once you have found this out, you must then divided that number by 45. Then you should have your answer. I guess you would rather me give you the answer, I am under Galatiain law, never to reveal this answer, if I did the entire Querns race would be in jeopardy.

Answer 3

See my answer on your previous question. Next time label your question with abstract algebra to attract the right attention.

Answer 4

Sounds painful..Good luck.

Answer 5

I have a headache and I'm overwhelmed by your intellligence.

Answer 6

yah

Answer 7

BOY..................DO IT YOURSELF.....................DO U THINK WE WILL DO THE HOMEWORK FOR U ................NO WAY