- #1

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## Homework Statement

Let G be a finite group and let I ={g in G: g^2 = e} \ {e} be its subset of involutions. Show that G is abelian if card(I) => (3/4)card(G).

## Homework Equations

## The Attempt at a Solution

I don't really know how to proceed with this problem and to make use of 3/4. I know that the set I is precisely the elements of order 2 in the group G and all elements within I U {e} commute; but I just don't know how to show the whole group commutes. Any help on how to proceed with the problem is highly appreciated. Thanks.