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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 ...
Wikipedia:Random. On Wikipedia and other sites running on MediaWiki, Special:Random can be used to access a random article in the main namespace; this feature is useful as a tool to generate a random article. Depending on your browser, it's also possible to load a random page using a keyboard shortcut (in Firefox, Edge, and Chrome Alt-Shift + X ).
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.
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 ...
This page was last edited on 14 July 2005, at 18:29 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike License 4.0; additional terms may ...
A group that is generated by a single element is called cyclic. Every infinite cyclic group is isomorphic to the additive group of the integers Z . A locally cyclic group is a group in which every finitely generated subgroup is cyclic. The free group on a finite set is finitely generated by the elements of that set ( §Examples ).
In mathematics, an automatic group is a finitely generated group equipped with several finite-state automata. These automata represent the Cayley graph of the group. That is, they can tell if a given word representation of a group element is in a "canonical form" and can tell if two elements given in canonical words differ by a generator. [1 ...
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.