Question

V. More Orders. Let a,b,c be elements of a group G. (i). If ord(a)= 15, what can ord(alº) equal? (ii). If ord(56)= 7, what ca

0 0
Add a comment Improve this question Transcribed image text
Know the answer?
Add Answer to:
V. More Orders. Let a,b,c be elements of a group G. (i). If ord(a)= 15, what...
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. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • (iii). Assume G is abelian. If ord(a)= 15 and ord(c)= 5, what can ord(ac) equal?

    (iii). Assume G is abelian. If ord(a)= 15 and ord(c)= 5, what can ord(ac) equal?

  • Always give rigorous arguments I. (A) Let G be a group under * and let g...

    Always give rigorous arguments I. (A) Let G be a group under * and let g E G with o(g) = n (finite) (i) Show that g can never go back to any previous positive power of g* (1k< n) when taking up to the nth power (cf. g), e., that there are no integers k and m such that 1< k<m<n and such that g*-gm (ii) How many elements of the set (e, g,g2.... .g"-) are actually distinct? (iii)...

  • Question 4 a) If a group G has order 323, what are the possible orders of...

    Question 4 a) If a group G has order 323, what are the possible orders of its proper b) Let G<a > be a cyclic group of order 10. Is the map f: G-> G define«d subgroups: by Зі i. f(a) - a and f(a')-a agroup isomorphism? ii(a) and fa a a group isomorphism? 12, 5, 5

  • 3. Let G be a group containing 6 elements a, b, c, d, e, and f....

    3. Let G be a group containing 6 elements a, b, c, d, e, and f. Under the group operation called the multiplication, we know that ad = c, bd = f, and f2 = bc = e. We showed you in class that the identity is e, hence the e-row and e-column were revealed. Using associativity, we also found cb, cf, af, and a2. Now try to imitate the idea and find five more entries. Justify your answer. Hint:...

  • Let a and b be elements of a group G such that b has order 2...

    Let a and b be elements of a group G such that b has order 2 and ab=ba^-1 12. Let a and b be elements of a group G such that b has order 2 and ab = ba-1. (a) Show that a” b = ba-n for all integers n. Hint: Evaluate the product (bab)(bab) in two different ways to show that ba+b = a-2, and then extend this method. (b) Show that the set S = {a”, ba" |...

  • 4) Let G be a group and let a є G. The centralizer of a in...

    4) Let G be a group and let a є G. The centralizer of a in G is defined as the set (i) Show that Ca(a) is a subgroup of G (ii) Find the centralizers of the elements r and y in the Dihedral group D4

  • 2. Let G be an abelian group. Suppose that a and b are elements of G...

    2. Let G be an abelian group. Suppose that a and b are elements of G of finite order and that the order of a is relatively prime to the order of b. Prove that <a>n<b>= <1> and <a, b> = <ab> .

  • Problem 4. Let G be a group. Recall that the order of an element g G...

    Problem 4. Let G be a group. Recall that the order of an element g G is the smallest k such that gk = 1 (or 00, if such a k doesn't exist). (a) Find the order of each element of the symmetric group S (b) Let σ-(135)(24) and τ-(15)(23)(4) be permutations in S5. Find the cycle decompositions for (c) Let σ-(123456789). Compute ơ-i, σ3, σ-50, and σί006 (d) Find all numbers n such that Ss contains an element of...

  • Let G be a group of order 6 and let X be the set (a, b,c) E G3: abc That is, X is the set of trip...

    Let G be a group of order 6 and let X be the set (a, b,c) E G3: abc That is, X is the set of triples of elements of G with the product of its coordinates equals the identity element of G (a) How many elements does X have? Hint: Every triple (a, b, c) in X is completely determined by the choice of a and b. Because once you choose a and b then c must be (ab)-1...

  • Let G be a group, and let a ∈ G. Let φa : G −→ G...

    Let G be a group, and let a ∈ G. Let φa : G −→ G be defined by φa(g) = aga−1 for all g ∈ G. (a) Prove that φa is an automorphism of G. (b) Let b ∈ G. What is the image of the element ba under the automorphism φa? (c) Why does this imply that |ab| = |ba| for all elements a, b ∈ G? 9. (5 points each) Let G be a group, and let...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT