Two new characteristic subgroups

Journal of Linear and Topological Algebra

دوره 12، شماره 04، اسفند 2023، صفحه 273-279   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.30495/jlta.2024.2000008.1598

نویسندگان

S. Barin؛ M. M. Nasrabadi^*

Department of Mathematics, University of Birjand, Birjand, Iran

چکیده

In this paper, we first define two new characteristic subgroups of a group $G$. Then we identify the relationships of these subgroups with $G'$, $S(G)$, $Ivar(G)$, and some different homomorphisms. Particularly, with one of these two subgroups, we determine the structure of $Ivar(G)$ and a subgroup of it that fixes $Z(G)$ element-wise.
 

کلیدواژه‌ها

$IA$-group؛ commutator subgroup؛ $IA$-central subgroup؛ $Ivar(G)$

مراجع

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[3] P. V. Hegarty, The absolute centre of a group, J. Algebra. 169 (1994), 929-935.

[4] J. Schur, Uber die darstellung der endlichen gruppen durch gebrochene lineare substitutionen, J. Reine Angew. Math. 127 (1904), 20-50.

[5] W. R. Scott, Group Theory, New York, Dover Publications, Inc, 1987.