if G be finite group and a be any element of G s.t. o(a)=n them a^m=e iff n|m
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If you're ambitious but lazy, please watch this video...
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If a and b are two elements of a.finite group G s.t.ab=ba and (o(a),o(b))=1 then o(ab)=o(a)o(b)
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If G be any group and a belongs to G be any element then o(a^k)=o(a)/(o(a),k)
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Semigroup and it's theorm
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A finite semigroup becomes group when both cancellation laws hold in it.
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7 Outside The Box Puzzles
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In a group of even order the number of elements of order 2 are odd
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