Characteristic of Free Groups

https://doi.org/10.22146/jmt.80513

Fitri Alfianti(1*)

(1) Gadjah Mada University
(*) Corresponding Author

Abstract


The set X of a group G is said to be a free generating set if every element of
G could be uniquely expressed as a product elements of X. A free group is defined as a containing set of free generating group. Furthermore, the set of free generators is referred to as a basis. Any two bases of a commutative free group have the same cardinality. One of the characteristics of the free group discussed in the study that any group is a factor group of a free group. Suppose m and n are cardinal numbers and n ≤ m, then Fm can be inserted into Fn. As a result a free group with a higher rank can be inserted into a free group with a lower rank. The presentation < S|R > is called a finite presentation if the sets S and R are finite sets. A group is said to be represented finitely if it has at least one finite presentation.


Keywords


group; free group; group presentation; free generating set; finite presentation

Full Text:

PDF Alfianti


References

Adhikari, M. R. 2016. Basic Algebraic Topology and Its Applications. Springer. India.

Dummit, D. S. dan Foote, R. M. 2004. Abstract Algebra. Third Edition. John Wiley and Sons, Inc. USA.

Goncalves, J. Z., Passman, D. S. 2015. Free Groups in Normal Subgroups of The Multiplicative Group of a Division Ring. Journal of Algebra. Vol. 440.

Hungerford, T. W. 1974. Algebra. Springer-Verlag New York, Inc. USA.

Malik, D. S. 1997, Fundamentals of Abstract Algebra. McGraw-Hill Companies, Inc., Singapore.

Malik, D. S., Modershon, J.N., dan Sen, M.K. 2007. An Introduction to Abstract Algebra. Creighton University. USA.

Pinter, C. A Book of Set Theory. Courier Corporation. US.

Rotman, J. J. 1995. An Introduction to the Theory of Groups. Fourth Edition. Springer-Verlag New York, Inc. USA.



DOI: https://doi.org/10.22146/jmt.80513

Article Metrics

Abstract views : 452 | views : 322

Refbacks

  • There are currently no refbacks.


Copyright of Jurnal Matematika Thales ISSN 2715-1891 (Print).

Jumlah Kunjungan: View My Stats


Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

JMT Indexed by: