plz with all details 6. Let G be a group and H a subgroup of G. Let a E G be an element Define aHa-1 ={aha-1|h E H}.A. Show that aHa-1 is also a subgroup of G.B. Suppose o(H)= n, what can you say about the order of o(aHa-1)?7. Let G be a group and a E G. The centralizer C(a) of a in G is define asC (a) xE G | χα αx)that is C(a) is the set of all elements in G which commutes with a. Show that C(a) is a subgroup ofG.

Name: plz with all details 6. Let G be a group and H a subgroup of G. Let a
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Description: plz with all details 6. Let G be a group and H a subgroup of G. Let a E G be an element Define aHa-1 ={aha-1|h E H}.A. Show that aHa-1 is also a subgroup of G.B. Suppose o(H)= n, what can you say about the order of o(aHa-1)?7. Let G be a group and a

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6. Let G be a group and H a subgroup of G. Let a E G be an element Define aHa-1 = {aha-1|h E H}. A. Show that aHa-1 is also a subgroup of G. B. Suppose o(H)= n, what can you say about the order of o(aHa-1)?

6. Let G be a group and H a subgroup of G. Let a E G be an element Define aHa-1 = {aha-1|h E H}. A. Show that aHa-1 is also a subgroup of G. B. Suppose o(H)= n, what can you say about the order of o(aHa-1)?

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 15E: Find groups H and K such that the following conditions are satisfied: H is a normal subgroup of K. K...

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