Intersections of Pure Subgroups in Abelian Groups
Copyright policy )Intersections of Pure Subgroups in Abelian Groups
It is shown that a subgroup H H of an abelian group G G is an intersection of pure subgroups of G G if and only if, for all primes p p and positive integers n n , p n g ∈ H {p^n}g \in H and p n − 1 g ∉ H {p^{n - 1}}g \notin H imply that there exists z ∈ G z \in G such that p n z = 0 {p^n}z = 0 and p n − 1 z ∉ H {p^{n - 1}}z \notin H . This solves a problem posed by L L . Fuchs in [2] and [3].
Chains and lattices of subgroups, subnormal subgroups, Subgroups of abelian groups, intersection of pure subgroups
Chains and lattices of subgroups, subnormal subgroups, Subgroups of abelian groups, intersection of pure subgroups
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