Unusual Way of Looking at a Finite Group as Subgroup of a Special Linear Group

Gaurav Mittal; Kanika Singla

doi:https://doi.org/10.14445/22315373/IJMTT-V53P522

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 53 | Number 3 | Year 2018 | Article Id. IJMTT-V53P522 | DOI : https://doi.org/10.14445/22315373/IJMTT-V53P522

Unusual Way of Looking at a Finite Group as Subgroup of a Special Linear Group

Gaurav Mittal, Kanika Singla

Abstract

In this paper we have proved that every group of finite order can be embedded in a normal subgroup of the group of invertible matrices over the field R, i.e., GL(n, R) for some n. The field we have taken, is R. But, we can also take Z, Q, C or finite fields instead of R. We have given the proof for embedding of An in SL(n, R) which is stronger result than the embedding of An in SL(n + 1, R). We have also shown that any group of finite order can be embedded in a perfect group.

Keywords

Embedding, General linear group, Perfect group, Special linear group, Alternating group.

References

[1] Basic Abstract Algebra, 2nd ed, P. B. Bhattacharya, S. K. Jain and S. R. Nagpaul, Cambridge University Press, 1994.
[2] Contemporary Abstract Algebra, 8th ed, Joseph A. Gallian, Thomson Brooks/Cole, 2012.

Citation :

Gaurav Mittal, Kanika Singla, "Unusual Way of Looking at a Finite Group as Subgroup of a Special Linear Group," International Journal of Mathematics Trends and Technology (IJMTT), vol. 53, no. 3, pp. 180-183, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V53P522