On groups with action on itself

Abstract

Abstract We introduce the notions of center, singularity and nilpotency (class) of a group with action on itself. Also, we describe a new package GwA for GAP4, including functions checking some properties of groups with action on itself with finite underlying group. As applications of the implemented functions, we give examples of groups with action satisfying Condition 1 stated in [3]. In other words, we get concrete examples of “coquecigrue” in the terminology of Loday [8, 9].