2. Let G = Z50 and consider it's subgroup H = (5). Find all coset representatives of 3 + H.

Answered: Image /qna-images/answer/5aa578bc-bb50-4588-be29-90b469eda8e6.jpg

Answered: 2. Let G = Z50 and consider it's…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.4: Cosets Of A Subgroup

Problem 11E: Let be a group of order 24. If is a subgroup of , what are all the possible orders of ?

See similar textbooks

Similar questions

Find all subgroups of the quaternion group.
Find two groups of order 6 that are not isomorphic.
Write 20 as the direct sum of two of its nontrivial subgroups.
4. List all the elements of the subgroupin the group under addition, and state its order.
4. Prove that the special linear group is a normal subgroup of the general linear group .
10. Find all normal subgroups of the octic group.
5. Exercise of section shows that is a group under multiplication. a. List the elements of the subgroupof , and state its order. b. List the elements of the subgroupof , and state its order. Exercise 33 of section 3.1. a. Let . Show that is a group with respect to multiplication in if and only if is a prime. State the order of . This group is called the group of units in and is designated by . b. Construct a multiplication table for the group of all nonzero elements in , and identify the inverse of each element.
2. Show that is a normal subgroup of the multiplicative group of invertible matrices in .
45. Let . Prove or disprove that is a group with respect to the operation of intersection. (Sec. )
Suppose G1 and G2 are groups with normal subgroups H1 and H2, respectively, and with G1/H1 isomorphic to G2/H2. Determine the possible orders of H1 and H2 under the following conditions. a. G1=24 and G2=18 b. G1=32 and G2=40
With H and K as in Exercise 18, prove that K is a normal subgroup of HK. Exercise18: If H is a subgroup of G, and K is a normal subgroup of G, prove that HK=KH.
Find the right regular representation of G as defined Exercise 11 for each of the following groups. a. G={ 1,i,1,i } from Example 1. b. The octic group D4={ e,,2,3,,,, }.

SEE MORE QUESTIONS

Recommended textbooks for you

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Elements Of Modern Algebra

Algebra

ISBN:

9781285463230

Author:

Gilbert, Linda, Jimmie

Publisher:

Cengage Learning,

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

SEE MORE TEXTBOOKS

2. Let G = Z50 and consider it's subgroup H = (5). Find all coset representatives of 3+ H.