Prove that there is no simple group of order 315 = 32 .5 . 7.

Q: Prove that there is no simple group of order 525 = 3 . 52 . 7.

A: To Prove: There is no simple group of order 525=3·52·7.

Q: Show that a group G of order pqr  for distinct primes, p,q and r, is  solvalbe.

A: |G| = pqr.   Without loss of generality, let p<q<r. We claim two things :  (i) There exists a…

Q: Prove that there is no simple group of order 396 = 22 .32 .11.

A: We have to prove that there is no simple group of order 396=22⋅32⋅11. We will prove this by the…

Q: 4.7 Let G= be a cyclic group of order 24. List all the elements in G that are of order 4.

A: Every element of G can be written as xa for some a between 0 and 23 (including both).  Suppose that…

Q: Show that there is no simple group of order pqr, where p, q, and rare primes ( p, q, and r need not…

A: We know the definition of simple group, A simple group is a group whose only normal subgroups are…

Q: Prove that there is no simple group of order 120 = 23 . 3 . 5.

A: We know the definition of simple group, A simple group is a group whose only normal subgroups are…

Q: Show that there are no simple groups of order 255 = (3)(5)(17).

A:

Q: What do the Sylow theorems tell you about any group of order 100?

A: Let G be a group of order 100.