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Full-Text Articles in Physical Sciences and Mathematics
On Projection-Invariant Subgroups Of Abelian P-Groups, Brendan Goldsmith
On Projection-Invariant Subgroups Of Abelian P-Groups, Brendan Goldsmith
Articles
A subgroup P of an Abelian p-group G is said to be projection-invariant in G if Pf is contained in P for all idempotent endomorphisms f. Clearly fully invariant subgroups are projection invariant, but the converse is not true in general. Hausen and Megibben have shown that in many familiar situations these two concepts coincide. In a different direction, the authors have previously introduced the notions of socle-regular and strongly socle-regular groups by focussing on the socles of fully invariant and characteristic subgroups of p-groups. In the present work the authors examine the socles of projection-invariant subgroups of Abelian p-groups.
On Super And Hereditarily Hopfian And Co-Hopfian Abelian Groups, Brendan Goldsmith, Katao Kong
On Super And Hereditarily Hopfian And Co-Hopfian Abelian Groups, Brendan Goldsmith, Katao Kong
Articles
The notions of Hopfian and co-Hopfian groups have been of interest for some time. In this present work we characterize the more restricted classes of hereditarily Hopfian (co-Hopfian) and super Hopfian (co-Hopfian) groups in the case where the groups are Abelian.