G is group and a,b be elements of G such that (o(a),o(b))=1 and ab=ba then o(ab)=o(a)o(b).

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a,b element of group G,ab=ba, then o(ab)=o(a).o(b) a,b element of group G,ab=ba, then o(ab)=o(a).o(b)
#Order of element #important theorem: O(ab) = O(a).O(b) if gcd(O(a), O(b)) = 1 and ab=ba #Order of element #important theorem: O(ab) = O(a).O(b) if gcd(O(a), O(b)) = 1 and ab=ba
O(ab)=O(a)*O(b) where g.c.d(O(a),O(b))=1 and ab=ba. O(ab)=O(a)*O(b) where g.c.d(O(a),O(b))=1 and ab=ba.
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) 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)
Group Theory - If a,b be any element of any group s.t ab=ba (o(a),o(b)) =1then o(ab) =o(a) o(b) Group Theory - If a,b be any element of any group s.t ab=ba (o(a),o(b)) =1then o(ab) =o(a) o(b)
O(ab)=O(ba) for all a,b in a Finite group G. O(ab)=O(ba) for all a,b in a Finite group G.
NET/GATE - Mathematics | Abstract Algebra | Question of the day | Question #180 NET/GATE - Mathematics | Abstract Algebra | Question of the day | Question #180
16. In a group G, let a,b and ab has order 2 then ab=ba 16. In a group G, let a,b and ab has order 2 then ab=ba