On subgroups of fixed index
Guy White · Pacific Journal of Mathematics · 1969
If ke St~, where J%Γ is a subgroup of a group S/ 7 y then closure implies k 2 , k 3 , , e J%Γ.Nonempty subsets Scy with the inverse property s m e S implies s, s 2 , , s m e S (m = 1, 2, •) will be called stellar sets.Let p a be a fixed prime power.If a stellar set S of an abelian group £f intersects every subgroup Sfc* of index p a in ,5/% and O^S, then the cardinal |S| of S is bounded below by p a (Theorem 3), when S^ satisfies a mild condition.