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###### Prerna Chaudhary posted an Question
October 14, 2021 • 23:53 pm 30 points
• IIT JAM
• Mathematics (MA)

## . prove that if an abelian group has more than three elements of order 2, then it has at least 7 elements of order 2. find an example that shows this is not tru

. Prove that if an Abelian group has more than three elements of order 2, then it has at least 7 elements of order 2. Find an example that shows this is not true for non-Abelian groups. d6 2 What are the possi1-

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• ##### Ishu 1

S3 is non Abelson group (1,2),(2,3),(3,1) are elements of order 2. no any other elements of order 2

• ##### Ishu 1

let a, b, c are elements of abelian group G of order 2 .then ab, ac,bc and abc are elements of G of order 2.bcz (ab) ²=a².b²=e. e=e .therefore G has at least 7 element a, b, c, ab, bc, ac, abc.

check it.

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