Two new characteristic subgroups
محورهای موضوعی : 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)
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.
[1] S. Bachmuth, Automorphisms of free metabelian groups, Trans. Amer. Math. Soc. 118 (1965), 93-104.
[2] R. G. Ghumde, S. H. Ghate, IA-automorphisms of p-groups, finite polycyclic groups and other results, Math. Ves. 67 (2015), 194-200.
[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.
