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Let G be a group. Let m be a positive integer, and let a1, a2, . . ., am be elements in G. What element is (a1a2...am)-1? Prove your answer through induction.  I understand that this is the inverse element, but I am a little confused how to show this through an induction proof. Thanks!

Let G be a group. Let m be a positive integer, and let a1, a2, . . ., am be elements in G. What element is (a1a2...am)-1? Prove your answer through induction.  I understand that this is the inverse element, but I am a little confused how to show this through an induction proof. Thanks!

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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Let G be a group. Let m be a positive integer, and let a1, a2, . . ., am be elements in G. What element is (a1a2...am)-1? Prove your answer through induction. 

I understand that this is the inverse element, but I am a little confused how to show this through an induction proof. Thanks!

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