Bachmuth defined an IA-automorphism of a group G as an automorphism of G which induces the identity automorphism on G/G'. Ghumde and Ghate introduced S(G) and Ivar(G) subgroups. In this paper, we first introduce a new series on the IA-central subgroup and verify the relationships of the members of this series. Also, we give a new definition for S(G)-autonilpotency on this series. Then, we discuss some properties of these concepts with some theorem and their corollaries. We investigate the members of Ivar(G) fixing the center element-wise. At the end of this paper, we study the conditions in which Ivar(G) relate to Inner automorphisms in S(G)-autonilpotent groups. Among the paper's innovations and contributions, we can mention the works [7] and [5] and the generalization of S(G)-Autonilpotent groups [6].
Barin, S. and Nasrabadi, M. M. (2026). The relationships of Ivar(G) with Inner automorphisms in S(G)-autonilpotent groups. Journal of Algebra and Related Topics, (), -. doi: 10.22124/jart.2026.29119.1737
MLA
Barin, S. , and Nasrabadi, M. M.. "The relationships of Ivar(G) with Inner automorphisms in S(G)-autonilpotent groups", Journal of Algebra and Related Topics, , , 2026, -. doi: 10.22124/jart.2026.29119.1737
HARVARD
Barin, S., Nasrabadi, M. M. (2026). 'The relationships of Ivar(G) with Inner automorphisms in S(G)-autonilpotent groups', Journal of Algebra and Related Topics, (), pp. -. doi: 10.22124/jart.2026.29119.1737
CHICAGO
S. Barin and M. M. Nasrabadi, "The relationships of Ivar(G) with Inner automorphisms in S(G)-autonilpotent groups," Journal of Algebra and Related Topics, (2026): -, doi: 10.22124/jart.2026.29119.1737
VANCOUVER
Barin, S., Nasrabadi, M. M. The relationships of Ivar(G) with Inner automorphisms in S(G)-autonilpotent groups. Journal of Algebra and Related Topics, 2026; (): -. doi: 10.22124/jart.2026.29119.1737
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