Affiliation:
1. Faculty of Mathematics and Technologies of Programming, Francisk Skorina Gomel State University, 104 Sovetskaya Str., 246019 Gomel, Belarus
Abstract
According to Foguel, a subgroup [Formula: see text] of a group [Formula: see text] is called conjugate-permutable if [Formula: see text] for every [Formula: see text]. Mingyao Xu and Qinhai Zhang studied finite groups with every subgroup conjugate-permutable (ECP-groups) and asked three questions about them. We gave the answers to these questions. In particular, every group of exponent 3 is an ECP-group, there exist non-regular ECP-[Formula: see text]-groups and the class of all finite ECP-groups is neither a formation nor a variety.
Publisher
World Scientific Pub Co Pte Lt