Question 4 Consider the group presentation (a,b,cla²bc², a¹bc¯¹, 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!)

Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter15: Deterministic Eoq Inventory Models
Section15.2: The Basic Economic Order Quantity Model
Problem 15P
Question
Question 4 Consider the group presentation
(a,b,cla²bc², a¹bc¯¹, 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!)
Transcribed Image Text:Question 4 Consider the group presentation (a,b,cla²bc², a¹bc¯¹, 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!)
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