Volume 19, Issue 1 (4-2024)                   IJMSI 2024, 19(1): 95-105 | Back to browse issues page

XML Print

Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

Khoshtarash R, Rajabzadeh Moghaddam M R, Rostamyari M A. Finite Groups with Specific Number of 2-Engelizers. IJMSI 2024; 19 (1) :95-105
URL: http://ijmsi.ir/article-1-1691-en.html
In 2016, the second and third authors introduced the notion of 2-Engelizer of the element x in a given group G and denoted the set of all 2-Engelizers in G by E2(G). They also constructed the possible values of |E2(G)| [Bull. Korean Math. Soc., 53(3), (2016), 657-665]. In the present paper, we classify all non 2-Engel finite groups G, when |E2(G)| = 4, 5.
Type of Study: Research paper | Subject: Special

1. A. Abdollahi, Engel Elements in Groups, In C. Campbell, M. Quick, E. Robertson, C. Roney-Dougal, G. Smith, G. Traustason (Eds.), Groups St Andrews 2009 in Bath (London Mathematical Society Lecture Note Series, pp. 94-117). Cambridge: Cambridge University Press.
2. A. R. Ashrafi, On Finite Groups with a Given Number of Centralizers, Algebra Colloq., 7(2), (2000), 139-146 [DOI:10.1007/s10011-000-0139-5]
3. S. M. Belcastro, G. J. Sherman, Counting Centralizers in Finite Groups, Math. Mag., 67(5), (1994), 366-374. [DOI:10.1080/0025570X.1994.11996252]
4. M. Bruckheimer, A. C. Bryan, A. Muir, Groups which Are the :union: of Three Subgroups, Amer. Math. Monthly, 77(1), (1970), 52-57. [DOI:10.1080/00029890.1970.11992416]
5. S. M. Jafarian Amiri, M. Amiri, H. Rostami, Finite groups determined by the number of element centralizers, Comm. Algebra, 45(9), (2017), 3792-3797. [DOI:10.1080/00927872.2016.1246664]
6. L.-C. Kappe, Right and Left Engel Elements in Metabelian Groups, Comm. Algebra, 9(12), (1981), 1295-1306. [DOI:10.1080/00927878108822647]
7. W. Kappe, Die A-Norm Einer Gruppe, Illinois J. Math., 5, (1961), 187-197. [DOI:10.1215/ijm/1255629817]
8. M. R. R. Moghaddam, M. A. Rostamyari, 2-Engelizer Subgroup of a 2-Engel Transitive Groups, Bull. Korean Math. Soc., 53(3), (2016), 657-665. [DOI:10.4134/BKMS.b140818]
9. D. J. S. Robinson, Finiteness Conditions and Generalized Soluble Groups, Part 2, Springer, 1972. [DOI:10.1007/978-3-662-11747-7]
10. G. Scorza, I Gruppi che Possono Pensarsi Come Somma di Tre Loro Sottogruppi, Boll. Un. Mat. It., 5, (1926), 216-218.

Add your comments about this article : Your username or Email:

Rights and permissions
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

© 2024 CC BY-NC 4.0 | Iranian Journal of Mathematical Sciences and Informatics

Designed & Developed by : Yektaweb