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Question 4 Consider the group presentation 1 (a,b,cla²b²c², a¹bc¹,aba¯¹b-¹). Show that, modulo the relations, we have ba²cb¹abc²= = e. Show all steps. (Hint: Try inserting a¹bc¹ between some letters and see how this goes. Also, note that the relation aba-¹b-¹ tells us that ab = ba, it can be very useful!)

Question 4 Consider the group presentation 1 (a,b,cla²b²c², a¹bc¹,aba¯¹b-¹). Show that, modulo the relations, we have ba²cb¹abc²= = e. Show all steps. (Hint: Try inserting a¹bc¹ between some letters and see how this goes. Also, note that the relation aba-¹b-¹ tells us that ab = ba, it can be very useful!)

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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I first tried to insert a^-1bc^-1 as described in the hint and then I inserted aba^-1b^-1 and then started switching a and b with the property that ab = ba but I somehow always get stuck at the same place...

 

Question 4 Consider the group presentation (a,b,cla²b²c², a-¹bc¹,aba-¹b-¹). Show that, modulo the relations, we have ba²cb-¹abc² = e. Show all steps. (Hint: Try inserting a-¹bc-¹ between some letters and see how this goes. Also, note that the relation aba-¹b-¹ tells us that ab = ba, it can be very useful!)
Transcribed Image Text:Question 4 Consider the group presentation (a,b,cla²b²c², a-¹bc¹,aba-¹b-¹). Show that, modulo the relations, we have ba²cb-¹abc² = e. Show all steps. (Hint: Try inserting a-¹bc-¹ between some letters and see how this goes. Also, note that the relation aba-¹b-¹ tells us that ab = ba, it can be very useful!)
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