Prove or disprove this statement. If G is a group in which every proper subgroup is cyclic, then G is cyclic.

Q: Prove the next statement: If G is an abelian group of finite order n, then G has a subgroup of…

A: Answer

Q: Every subgroup of an abelian group is normal.

A: We have to prove that every subgroup of abelian is normal subgroup.

Q: subgroup and homomorphic image of a solvable group is solvable.

A:

Q: An element g of G is called idempotent if g2 = g. (1) Show that every group has at least one…

A: For the solution of the problem follow the next steps.

Q: Suppose that G is an Abelian group with an odd number of elements.Show that the product of all of…

A:

Q: For any group G then G/Z(G) is abelin Select one: O True O False

A:

Q: Let (G1, •) and (G2 , *) be two groups and p : G1 – G2 be an isomorphism. Then * O G2 is finite if…

A: We will use basic results of group theory

Q: Which of the following statement is true? Every function is a permutation if and only if it is onto…

A: We find which of the following statement is true.

Q: Show that a group of order 77 is cyclic.

A: