A note on infinite -groups
Let be a group. If every nontrivial subgroup of has a proper supplement, then is called an -group. We study some properties of -groups. For instance, it is shown that a nilpotent group is an -group if and only if is a subdirect product of cyclic groups of prime orders. We prove that if is an -group which satisfies the descending chain condition on subgroups, then is finite. Among other results, we characterize all abelian groups for which every nontrivial quotient group is an -group....