Vol. 28, No. 1, 1969

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On subgroups of fixed index

G. K. White

Vol. 28 (1969), No. 1, 225–232
Abstract

If k ∈𝒦, where 𝒦 is a subgroup of a group 𝒮 , then closure implies k2,k3,,∈𝒦. Nonempty subsets S ⊂𝒮 with the inverse property sm S implies s,s2,,sm S (m = 1,2,) will be called stellar sets. Let pα be a fixed prime power. If a stellar set S of an abelian group 𝒮 intersects every subgroup of index pα in 𝒮 , and 0S, then the cardinal |S| of S is bounded below by pα (Theorem 3), when 𝒮 satisfies a mild condition.

Mathematical Subject Classification
Primary: 20.30
Milestones
Received: 13 October 1967
Published: 1 January 1969
Authors
G. K. White