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 .
Read more about Absolute Presentation Of A Group: Formal Definition, Example, Background
Famous quotes containing the words absolute, presentation and/or group:
“Pharisaism, obtuseness and tyranny reign not only in the homes of merchants and in jails; I see it in science, in literature, and among youth. I consider any emblem or label a prejudice.... My holy of holies is the human body, health, intellect, talent, inspiration, love and the most absolute of freedoms, the freedom from force and falsity in whatever forms they might appear.”
—Anton Pavlovich Chekhov (1860–1904)
“He uses his folly like a stalking-horse, and under the presentation of that he shoots his wit.”
—William Shakespeare (1564–1616)
“Jury—A group of twelve men who, having lied to the judge about their hearing, health, and business engagements, have failed to fool him.”
—H.L. (Henry Lewis)