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Presentation of a group. In mathematics, a presentation is one method of specifying a group. A presentation of a group G comprises a set S of generators —so that every element of the group can be written as a product of powers of some of these generators—and a set R of relations among those generators. We then say G has presentation.
Rubric (academic) In the realm of US education, a rubric is a "scoring guide used to evaluate the quality of students' constructed responses" according to James Popham. [1] In simpler terms, it serves as a set of criteria for grading assignments. Typically presented in table format, rubrics contain evaluative criteria, quality definitions for ...
PechaKucha (Japanese: ぺちゃくちゃ, IPA: [petɕa kɯ̥tɕa], [1] chit-chat) is a storytelling format in which a presenter shows 20 slides for 20 seconds per slide. At a PechaKucha Night, individuals gather at a venue to share personal presentations about their work. The PechaKucha format can be used, for example, in business presentations ...
Absolute presentation of a group. 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 ...
Group isomorphism problem. In abstract algebra, the group isomorphism problem is the decision problem of determining whether two given finite group presentations refer to isomorphic groups . The isomorphism problem was formulated by Max Dehn, [1] and together with the word problem and conjugacy problem, is one of three fundamental decision ...
A rubric is a word or section of text that is traditionally written or printed in red ink for emphasis. The word derives from the Latin rubrica, meaning red ochre or red chalk, [1] and originates in medieval illuminated manuscripts from the 13th century or earlier. In these, red letters were used to highlight initial capitals (particularly of ...
A set-theoretic representation (also known as a group action or permutation representation) of a group G on a set X is given by a function ρ : G → XX, the set of functions from X to X, such that for all g1, g2 in G and all x in X: ρ x x. ρ x ρ ρ x. where is the identity element of G.
In the mathematical subject of geometric group theory, a Dehn function, named after Max Dehn, is an optimal function associated to a finite group presentation which bounds the area of a relation in that group (that is a freely reduced word in the generators representing the identity element of the group) in terms of the length of that relation (see pp. 79–80 in [1]).
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