Absolute Presentation Of A Group
In mathematics, one method of defining a group is by an absolute presentation.
Recall that to define a group by means of a presentation, one specifies a set of generators so that every element of the group can be written as a product of some of these generators, and a set of relations among those generators. In symbols:
Informally is the group generated by the set such that for all . But here there is a tacit assumption that is the "freest" such group as clearly the relations are satisfied in any homomorphic image of . One way of being able to eliminate this tacit assumption is by specifying that certain words in should not be equal to That is we specify a set, called the set of irrelations, such that for all .
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