On Group of Inner Automorphisms of Some
𝐶𝑛 -groups

Shelly Khurana; Ankur Bala

doi:https://doi.org/10.14445/22315373/IJMTT-V44P516

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 44 | Number 2 | Year 2017 | Article Id. IJMTT-V44P516 | DOI : https://doi.org/10.14445/22315373/IJMTT-V44P516

On Group of Inner Automorphisms of Some 𝐶𝑛 -groups

Shelly Khurana, Ankur Bala

Abstract

Let G be an arbitrary 𝐶𝐶𝑛𝑛 -group, where 𝐶𝐶𝑛𝑛 -groups are groups with 𝑛𝑛 number of centralizers &𝑛𝑛 is any finite number. In this article, we have proved that the group of inner automorphisms of G is isomorphic to some other groups depending upon𝑛𝑛. Moreover if for some group 𝐺𝐺, the group of inner automorphisms 𝐼𝐼𝐼𝐼𝐼𝐼(𝐺𝐺) has order 6 or 9 then 𝐺𝐺 will be 𝐶𝐶5-group and if for some group 𝐻𝐻 , the group of inner automorphisms 𝐼𝐼𝐼𝐼𝐼𝐼(𝐻𝐻) has order 4 then 𝐻𝐻 will be 𝐶𝐶4-group & conversely.

Keywords

where Cn-groups are groups with n number of number of centralizers & n is any finite number.

References

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Citation :

Shelly Khurana, Ankur Bala, "On Group of Inner Automorphisms of Some 𝐶𝑛 -groups," International Journal of Mathematics Trends and Technology (IJMTT), vol. 44, no. 2, pp. 80-83, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V44P516