suppose that a,b are elements of a group and a^5=e, b^4=e, ab=ba^3
Prove that (i) a^b =ba (ii) ab^3=b^3a^2

Question

suppose that a,b are elements of a group and a^5=e, b^4=e, ab=ba^3
Prove that (i) a^b =ba   (ii) ab^3=b^3a^2

perl · Answer

you sure there are no typos, for part a) a^b = ba ?

perl · Answer

so this is like a puzzle

perl · Answer

apply multiplication on both sides

anonymous · Answer

dont understand

perl · Answer

ab=ba^3

multiply both sides by a^2 (on the right)
ab *a^2 = b*a^3 * a^2 

aba^2 = b* a^5
aba^2 = b*e 
aba^2 = b

perl · Answer

ab=ba^3
multiply both sides by a^2 (on the right)
ab *a^2 = b*a^3 * a^2
ab*a^2 = b* a^5 
aba^2 = b*e
aba^2 = b

perl · Answer

i think you can make a table

perl · Answer

i will be able to answer more quickly if i see the original worksheet or problem

perl · Answer

can you take a picture of the question and upload it?

anonymous · Answer

i cant it was written down on a piece of paper