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Random group. In mathematics, random groups are certain groups obtained by a probabilistic construction. They were introduced by Misha Gromov to answer questions such as "What does a typical group look like?" It so happens that, once a precise definition is given, random groups satisfy some properties with very high probability, whereas other ...
The 5th roots of unity in the complex plane form a group under multiplication. Each non-identity element generates the group. In abstract algebra, a generating set of a group is a subset of the group set such that every element of the group can be expressed as a combination (under the group operation) of finitely many elements of the subset and their inverses.
Random assignment. Random assignment or random placement is an experimental technique for assigning human participants or animal subjects to different groups in an experiment (e.g., a treatment group versus a control group) using randomization, such as by a chance procedure (e.g., flipping a coin) or a random number generator. [ 1]
Generator (mathematics) The 5th roots of unity in the complex plane under multiplication form a group of order 5. Each non-identity element by itself is a generator for the whole group. In mathematics and physics, the term generator or generating set may refer to any of a number of related concepts. The underlying concept in each case is that ...
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.
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Random number generation is a process by which, often by means of a random number generator ( RNG ), a sequence of numbers or symbols that cannot be reasonably predicted better than by random chance is generated. This means that the particular outcome sequence will contain some patterns detectable in hindsight but impossible to foresee.
Later Dunfield and Thurston proved [31] that if a one-relator two-generator group = , = is chosen "at random" (that is, a cyclically reduced word r of length n in (,) is chosen uniformly at random) then the probability that a homomorphism from G onto with a finitely generated kernel exists satisfies