Answered: 7. Show that the subgroup H = {1, −1}… | bartleby

Elements Of Modern Algebra

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.5: Normal Subgroups

Problem 12E: 12. Find all normal subgroups of the quaternion group.

See similar textbooks

Related questions

Question

7. Show that the subgroup H = {1, −1} of the quaternion group Q is normal. Construct a Cayley
table for the quotient group Q/H.

Expert Solution

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

Find all subgroups of the quaternion group.
Find all homomorphic images of the quaternion group.
Find the normalizer of the subgroup (1),(1,3)(2,4) of the octic group D4.
4. Prove that the special linear group is a normal subgroup of the general linear group .
45. Let . Prove or disprove that is a group with respect to the operation of intersection. (Sec. )
Let H1={ [ 0 ],[ 6 ] } and H2={ [ 0 ],[ 3 ],[ 6 ],[ 9 ] } be subgroups of the abelian group 12 under addition. Find H1+H2 and determine if the sum is direct.
Let A={ a,b,c }. Prove or disprove that P(A) is a group with respect to the operation of union. (Sec. 1.1,7c)
Let G be a group with center Z(G)=C. Prove that if G/C is cyclic, then G is abelian.
9. Suppose that and are subgroups of the abelian group such that . Prove that .
Find two groups of order 6 that are not isomorphic.
Show that every subgroup of an abelian group is normal.
1. Consider H= (i) and K= (-1) the subgroups of Q, the quaternion group. 4) Explain why K is normal in Qs and find its normalizer.. 5) Find all elements of Q/K and determine the order of each element. 6) Find the group that is isomorphic to Q/K.

SEE MORE QUESTIONS

Recommended textbooks for you

Elements Of Modern Algebra

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

Elements Of Modern Algebra

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

SEE MORE TEXTBOOKS