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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2017: 0.23

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1572-9176
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On groups with action on itself

Enver Önder Uslu
  • Department of Mathematics and Computer Sciences, Art and Science Faculty, Eskisehir Osmangazi University, Eskisehir, Turkey
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/ Ahmet Faruk Aslan
  • Department of Mathematics and Computer Sciences, Art and Science Faculty, Eskisehir Osmangazi University, Eskisehir, Turkey
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/ Alper OdabaşORCID iD: http://orcid.org/0000-0002-4361-3056
Published Online: 2017-08-15 | DOI: https://doi.org/10.1515/gmj-2017-0036

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].

Keywords: Center; central series; ideal; nilpotency; groups with action

MSC 2010: 16W99; 17A32; 18D35

References

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    J.-L. Loday, Une version non commutative des algèbres de Lie: les algèbres de Leibniz, Enseign. Math. (2) 39 (1993), no. 3–4, 269–293. Google Scholar

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    The GAP Group, “GAP – Groups, Algorithms, and Programming, Version 4” 1997, Lehrstuhl D für Mathematik, RWTH Aachen, Germany and School of Mathematical and Computational Sciences, University of St. Andrews, Scotland, http://www-gap.dcs.st-and.ac.uk/~gap/.

About the article

Received: 2015-02-10

Revised: 2016-02-04

Accepted: 2016-02-24

Published Online: 2017-08-15


Funding Source: Eskisehir Osmangazi University Scientific Research Projects

Award identifier / Grant number: 2015-763

The third author was supported by Eskisehir Osmangazi University Scientific Research Projects (Grant no. 2015-763).


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2017-0036.

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