Definition:Group Presentation/Relation
< Definition:Group Presentation(Redirected from Definition:Relation of Group Presentation)
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Definition
The standard form of a relation in a group presentation is:
- $w = e$
where $w$ is a word in the group.
Also known as
A relation in a group presentation is also known as a defining relation.
It is also known as a relator.
Sources
- 1996: John F. Humphreys: A Course in Group Theory ... (previous) ... (next): Chapter $4$: Subgroups: Example $4.10$
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): relation: 4.
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): generator: 2. (of a group)
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): relation: 2. (in a group)
- 2000: Pierre A. Grillet: Abstract Algebra: $\S \text{I}.7$: Presentations
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): generator: 2. (of a group)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): relation: 2. (in a group)