What is "z-group"

In mathematics, especially in the area of algebra known as group theory, the term Z-group refers to a number of distinct types of groups:

• in the study of finite groups, a Z-group is a finite groups whose Sylow subgroups are all cyclic.
• in the study of infinite groups, a Z-group is a group which possesses a very general form of central series.
• occasionally, (Z)-group is used to mean a Zassenhaus group, a special type of permutation group.