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Fully inert subgroups of Abelian p-groups

Authors
Journal
Journal of Algebra
0021-8693
Publisher
Elsevier
Publication Date
Volume
419
Identifiers
DOI: 10.1016/j.jalgebra.2014.07.021
Keywords
  • Fully Inert Subgroups
  • Direct Sums Of Cyclic P-Groups
  • Fully Invariant Subgroups
  • Commensurable Subgroups

Abstract

Abstract A subgroup H of an Abelian group G is said to be fully inert in G, if for every endomorphism ϕ of G, the factor group (H+ϕ(H))/H is finite. This notion arises in the study of the dynamical properties of endomorphisms (entropy). The principal result of this work is that fully inert subgroups of direct sums of cyclic p-groups are commensurable with fully invariant subgroups of the direct sum.

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