Question

let G be a group of order 18. x, y, and z are elements of G....

let G be a group of order 18. x, y, and z are elements of G. if | < x, y >| = 9 and o(z) = order of z = 9, prove that G = < x, y, z >

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
8.4: Let f : X → Y and g : Y→ Z be maps. Prove that...
8.4: Let f : X → Y and g : Y→ Z be maps. Prove that if composition g o f is surjective then g is surjective. 8.5: Let f : X → Y and g : Y→ Z be bijections. Prove that if composition g o f is bijective then f is bijective. 8.6: Let f : X → Y and g : Y→ Z be maps. Prove that if composition g o f is bijective then f is...
Let G be a group. Define Z(G) ={x∈G|xg=gx for all g∈G}, that is Z(G) is the...
Let G be a group. Define Z(G) ={x∈G|xg=gx for all g∈G}, that is Z(G) is the set of elements commuting with all the elements of G. We call Z(G) the center of G. (In German, the word for center is Zentrum, hence the use of the “Z”.) (a) Show that Z(G) is a subgroup of G. (b) Show that Z(G) is an abelian group.
Let G be a group and let a ∈ G. The set CG(a) = {x ∈...
Let G be a group and let a ∈ G. The set CG(a) = {x ∈ G | xa = ax} of all elements that commute with a is called the Centralizer of a in G. (b) Compute CG(a) when G = S3and a = (1, 2). (c) Compute CG(a) when G = S4 and a = (1, 2). (d) Prove that Z(G) = ∩a∈GCG(a).
Using field and order axioms prove the following theorems: (i) Let x, y, and z be...
Using field and order axioms prove the following theorems: (i) Let x, y, and z be elements of R, the a. If 0 < x, and y < z, then xy < xz b. If x < 0 and y < z, then xz < xy (ii) If x, y are elements of R and 0 < x < y, then 0 < y ^ -1 < x ^ -1 (iii) If x,y are elements of R and x <...
Let G be a graph with x, y, z є V(G). Prove that if G contains...
Let G be a graph with x, y, z є V(G). Prove that if G contains an x, y-path and a y, z-path, then it contains an x, z-path.
Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}....
Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}. a) Prove or disprove: A ⊆ X b) Prove or disprove: X ⊆ A 4 c) Prove or disprove: P(X ∪ Y ) ⊆ P(X) ∪ P(Y ) ∪ P(X ∩ Y ) d) Prove or disprove: P(X) ∪ P(Y ) ∪ P(X ∩ Y ) ⊆ P(X ∪ Y )
Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}....
Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}. a) Prove or disprove: A ⊆ X b) Prove or disprove: X ⊆ A c) Prove or disprove: P(X ∪ Y ) ⊆ P(X) ∪ P(Y ) ∪ P(X ∩ Y ) d) Prove or disprove: P(X) ∪ P(Y ) ∪ P(X ∩ Y ) ⊆ P(X ∪ Y )
Let G = <a> be a cyclic group of order 12. Describe explicitly all elements of...
Let G = <a> be a cyclic group of order 12. Describe explicitly all elements of Aut(G), the group of automorphisms of G. Indicate how you know that these are elements of Aut(G) and that these are the only elements of Aut(G).
Let G be an Abelian group. Let k ∈ Z be nonzero. Define φ : G...
Let G be an Abelian group. Let k ∈ Z be nonzero. Define φ : G → G by φ(x) = x^ k . (a) Prove that φ is a group homomorphism. (b) Assume that G is finite and |G| is relatively prime to k. Prove that Ker φ = {e}.
Let G be a group of order p^3. Prove that either G is abelian or its...
Let G be a group of order p^3. Prove that either G is abelian or its center has exactly p elements.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT