Two new characteristic subgroups
محورهای موضوعی : Group theory
S. Barin
1
,
M. M. Nasrabadi
2
1 - Department of Mathematics, University of Birjand, Birjand, Iran
2 - Department of Mathematics, University of Birjand, Birjand, Iran
کلید واژه: $IA$-group, commutator subgroup, $IA$-central subgroup, $Ivar(G)$,
چکیده مقاله :
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.
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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