Two new characteristic subgroups

Subject Areas : Group theory

S.  Barin ¹ (Department of Mathematics, University of Birjand, Birjand, Iran)
M. M.  Nasrabadi ² (Department of Mathematics, University of Birjand, Birjand, Iran)

Received: 2023-10-28 Accepted : 2024-01-15 Published : 2024-02-14

Keywords: $IA$-group, commutator subgroup, $IA$-central subgroup, $Ivar(G)$,

Abstract :

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.

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