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Show that a group is abelian if and only if (ab)^2=a^2b^2 for all a,b in G If G is a group such that x.x=e for all x∈G then G is an abelian group Show that the set {1,2,4,5,7,8} is Group under multiplication modulo 9 If order of element x is odd then there exists element y such that y^2=x Show that a group of even order has an element of order 2 Orders of a and b^-1ab are equal (proof) Orders of a and a^-1 are equal | Orders of element and its inverse are same In this video you will learn Order of a group | Order of an element | Fully Concept Explained | Must watch Group Theory Abstract Algebra lectures Order of Group explained Order of an element explained bsc Bsc mathematical methods chapter 2 Group theory lectures in Hindi What is group in mathematics? Definition of Group in Hindi Group Definition Abelian Group Full Playlist of Group Theory https://www.youtube.com/watch?v=_pzEOUFUmlAu0026list=PL_BDyLp3D8n3aMmMdJijt2rEmXtwE-ZUf
17. Show that a group is abelian if and only if (ab)^2=a^2b^2 for all a,b in G17. Show that a group is abelian if and only if (ab)^2=a^2b^2 for all a,b in G17. Show that a group is abelian if and only if (ab)^2=a^2b^2 for all a,b in G17. Show that a group is abelian if and only if (ab)^2=a^2b^2 for all a,b in G
17. Show that a group is abelian if and only if (ab)^2=a^2b^2 for all a,b in G