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4. Let G be a group, and let g, h E G. Use Homework 3, Textbook Exercise 2.2 #24 to show that if gh = hg-¹, then gh = hgk for all k € Z (including negative k).

4. Let G be a group, and let g, h E G. Use Homework 3, Textbook Exercise 2.2 #24 to show that if gh = hg-¹, then gh = hgk for all k € Z (including negative k).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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24. Let a and b be elements of a group G. Prove that (aba-¹)k = abka-¹ holds for all kEZ (including negative k). DK Tf 5 1 and ¹ - m in a group, prove that bm5-1 = 1. [Hint: Exercise 24.] a-¹ha
Transcribed Image Text:24. Let a and b be elements of a group G. Prove that (aba-¹)k = abka-¹ holds for all kEZ (including negative k). DK Tf 5 1 and ¹ - m in a group, prove that bm5-1 = 1. [Hint: Exercise 24.] a-¹ha
4. Let G be a group, and let g, h E G. Use Homework 3, Textbook Exercise 2.2 #24 -1 to show that if gh = hg¯¹, then gh = hg-k for all k € Z (including negative k).
Transcribed Image Text:4. Let G be a group, and let g, h E G. Use Homework 3, Textbook Exercise 2.2 #24 -1 to show that if gh = hg¯¹, then gh = hg-k for all k € Z (including negative k).
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