Absolute presentation of a group
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In mathematics, an absolute presentation is one method of defining a group.[1]
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