Let po(3), where is a finite group and pany prime number. Then a Sylow p-sub group Hof Gis normal if His unique Sylow p-sub- group of G.

Q: If pq and r are three distinct primes and G is a group of order par, then G is not simple.

A: Suppose that p,q and r are three distinct primes and G is a group of order pqr, then prove that G is…

Q: Show that a group of order pn, where p is prime, is solvable.

A: Let G be a group of order p^n, where p is a prime number.We will prove by induction on n that G is…

Q: Show that a group G of order pq for  distinct primes p and q is solvable.

A: Introduction: A solvable group is a group having a normal series such that each normal factor is…

Q: Verify the corollary to the Fundamental Theorem of FiniteAbelian Groups in the case that the group…

A: To verify corollary to the Fundamental Theorem Of Finite Abelian Groups Where, G is a group of order…