1.6.41 Fields, Groups, Rings

Condition: let \ (x \)-the subset of the group \ (g \) such that \ (x x \ subseteq x \) (i.e. \ (x y \ in x; \ forall x, y \ in x \)). To prove that: 1) if \ (x \) of course or consists of periodic elements, then \ (x \)-subgroup \ (g \), 2) in the general case \ (x \) may not be a subgroup \ (g \).