It is easy to see that the number of involutions in an elementary abelian $2$-group of finite rank $n$ is $2^n-1$. Is there a formular for computing the number of involutions in any finite abelian group or precisely, is there any bound on the number of involutions in finite abelian groups $G$ in terms of $|G|$?
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In particular, I am interested in knowing whether we have any good bound on the proportion of involutions in an arbitrary abelian group of order n which is non-cyclic? – Chuks Dec 18 '16 at 10:14