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

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

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