Case Study of the Group𝐺𝐺𝐺𝐺(𝑛𝑛, ℤ )

Shelly khurana; Ankur Bala

doi:https://doi.org/10.14445/22315373/IJMTT-V44P517

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 44 | Number 2 | Year 2017 | Article Id. IJMTT-V44P517 | DOI : https://doi.org/10.14445/22315373/IJMTT-V44P517

Case Study of the Group𝐺𝐺𝐺𝐺(𝑛𝑛, ℤ )

Shelly khurana, Ankur Bala

Abstract

In this Article, we have discussed some of the properties of the infinite non-abelian group 𝐺𝐺𝐺𝐺(𝑛𝑛, ℤ), 𝑛𝑛 ≥ 2. Such as the number of elements of order 2, number of subgroups of order 2 in this group and embedding of the 𝐺𝐺𝐺𝐺(𝑛𝑛, ℤ) in 𝐺𝐺𝐺𝐺(𝑚𝑚 , ℤ)∀ 𝑚𝑚 ≥ 𝑛𝑛, Moreover for every finite group 𝐺𝐺, there exists 𝑘𝑘 ∈ ℕ such that 𝐺𝐺𝐺𝐺(𝑘𝑘 , ℤ) has a subgroup isomorphic to the group 𝐺𝐺.

Keywords

Infinite non-abelian group, 𝐺𝐺𝐺𝐺(𝑛𝑛, ℤ)

References

[1] Contemporary Abstract Algebra, J.A. Gallian, Cengage Learning, 2016 .ISBN: 1305887859, 9781305887855
[2] Abstract Algebra (3rd Edition), David S. Dummit , Richard M. Foote, ISBN: 978-0-471-43334-7
[3] On Embedding of Every Finite Group into a Group of Automorphism IJMTT, Vol.37, Number 2, ISSN: 2231-5373
[4] A Course in Abstract Algebra, Vijay K. Khanna, S.K. Bhambri, Second Edition, Vikas Publishing House Pvt Limited, 1999, 070698675X, 9780706986754

Citation :

Shelly khurana, Ankur Bala, "Case Study of the Group𝐺𝐺𝐺𝐺(𝑛𝑛, ℤ )," International Journal of Mathematics Trends and Technology (IJMTT), vol. 44, no. 2, pp. 84-88, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V44P517