On the structure of certain types of Abelian groups (Q788116)

The authors provide a complete description of four types of Abelian groups: (1) Uniform groups: that is, \(A\cap B\neq 0\) for any two non-zero subgroups A and B of G; (2) hollow Abelian groups G: that is, every proper subgroup A of G is superfluous in G; (3) groups without a proper minimal cover. The main part of the paper deals with (4) complemented Abelian groups: G is complemented iff every subgroup A of G has a minimal complement B, i.e. \(A+B=G,\) and B'\(\subseteq B\) and \(A+B'=G\) imply \(B'=B\).