The relationships of Ivar(G) with Inner automorphisms in S(G)-autonilpotent groups

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.

کلیدواژه ها:

IA-group ، Ivar(G) ، inner automorphisms ، IA-central subgroup ، S(G)-autonilpotent groups