Group theory/Problems

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H)a,b e Z T)a•b=ab†ab-1†...a1†a0

a•b=b•a

=(b-1†1)•a

=(b-1)•a†a

=(b-1-1†1)•a†a

=(b-2†1)•a†a

=(b-2)•a†a†a

=(b-2)•a†ab-1†ab-2...

=(b-b)•a†ab†ab-1†...a1†a0

=0•a†ab†ab-1†...a1†a0

=0†ab†ab-1†...a1†a0

=0†ab†ab-1†...a1†a0

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