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The notions of Hopﬁan and co-Hopﬁan groups are well known in both non-commutative and Abelian group theory. In this work we begin a systematic investigation of natural generalizations of these concepts and, in the case of Abelian p-groups, give a complete characterization of the generalizations in terms of the original concepts.
Goldsmith, Brendan and Gong, Katao, "R-Hopﬁan and L-co-Hopﬁan Abelian Groups" (2017). Articles. 281.