Description of Abelian group
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Modern Algebra
Group Theory (VII)
To prove that if G is an abelian group, then for all a,b belongs to G and all integers n, (a.b)^n=a^n.b^n.
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Prove that if is an abelian group, then for all and all integers , .
Proof:- Let be arbitrary.
By hypothesis, is an abelian group,
which imply that ---------------------------------(1)
which imply that
and
For
Suppose where is any integer, then
For
Hence by mathematical induction,
for all ...
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- MSc, Kanpur University
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