University of Guilan Journal of Algebra and Related Topics 2345-3931 2026 04 05 The relationships of Ivar(G) with Inner automorphisms in S(G)-autonilpotent groups 9523 10.22124/jart.2026.29119.1737 EN S. Barin Department of Mathematics, University of Birjand, Birjand, Iran M. M. Nasrabadi Department of Mathematics, University of Birjand, Birjand, Iran Journal Article 2024 11 29 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]. https://jart.guilan.ac.ir/article_9523_57d16ba118ba22eb8690026d0c91d82b.pdf