Relative homological algebra and abelian groups
Carol Peercy Walker · Illinois Journal of Mathematics · 1966
pure.It has been shown (Log [15]) that a subgroup A of a group B is m-pure in B if and only if A is a summand of every subgroup C of B such that A c C and C/A is generated by a subset of cardinal less than m.The concept of a neat subgroup (due to Honda [11]) can be defined in an analogous fashion.Namely, A is a neat subgroup of B if and only if A is a summand of every sub-