145. there exists a finite abelian group g containing exactly 60 elements of order 2. (t/f) (tifr 2017)

we know O(a)|O(G) if G contain 2 order element then order of G is even. we know order of identity is one remaining elements order more then one. if G contain 2 order element then n...

Suppose the order of G is 2n. Since order of identity is always 1 i.e. |e|=1. So we have left only2n−1 element which is odd in number. Elements which are not their own inverses, th...