On groups with action on itself


Uslu E. O. , ASLAN A. F. , ODABAŞ A.

GEORGIAN MATHEMATICAL JOURNAL, vol.26, no.3, pp.459-470, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 3
  • Publication Date: 2019
  • Doi Number: 10.1515/gmj-2017-0036
  • Journal Name: GEORGIAN MATHEMATICAL JOURNAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.459-470
  • Eskisehir Osmangazi University Affiliated: Yes

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].