#Order of element #important theorem: O(ab) = O(a).O(b) if gcd(O(a), O(b)) = 1 and ab=ba

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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.
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)
Prove in a group, if ab = ba and have finite order, then gcd(|a|,|b|) = 1 iff |ab| = |a||b| Prove in a group, if ab = ba and have finite order, then gcd(|a|,|b|) = 1 iff |ab| = |a||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) 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)
For any group elements a and b, Prove that |ab|=|ba|,Joseph A. Gallian Ch-3 Ques-20,Abstract Algebra For any group elements a and b, Prove that |ab|=|ba|,Joseph A. Gallian Ch-3 Ques-20,Abstract Algebra
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.
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). 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).
o(a)=o(a^k).gcd of n and k | some theorems on order of an element | Bsc/Msc Mathematics | Ravina o(a)=o(a^k).gcd of n and k | some theorems on order of an element | Bsc/Msc Mathematics | Ravina