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In mathematics, in the realm of group theory, a group is said to be critical if it is not in the variety generated by all its proper subquotients, which includes all its subgroups and all its quotients. [1] Any finite monolithic A-group is critical. This result is due to Kovacs and Newman. [2] But not every monolithic group is critical. [3]
The sequence of the items is critical. The numbering has some independent meaning, for example in a listing of musical tracks on an album. Use a # symbol at the start of a line to generate a numbered list item (excepted as detailed in this section, this works the same as * for bulleted lists, above).
Stating the key judgment and significance up front sets up the argument, ensures the message is clear, and highlights why the reader should care about the document. In order to create a reader-friendly prose, writers structure their paragraphs using BLUF format to better aid the reader's ability to recall the paragraph's main idea or content.
Text formatting in citations should follow, consistently within an article, an established citation style or system. Options include either of Wikipedia's own template-based Citation Style 1 and Citation Style 2, and any other well-recognized citation system. Parameters in the citation templates should be accurate.
Bold text is stylistically offset from other text without conveying extra importance. The most common use of boldface is to highlight the article title, and often synonyms, in the lead section. Do not use bold text for emphasis. Use ''' to open and close bold text.
If the title has a parenthetical disambiguator, such as Mercury (planet), the parenthetical should be omitted in the text. [G] Dates and locations should be included in the first sentence if they help the reader to quickly determine if they're reading the right article. For instance, in the article Spanish–American War, the text of the lead ...
Structured criticality is a property of complex systems in which small events may trigger larger events due to subtle interdependencies between elements. This often gives rise to a form of stratified chaos where the general behavior of the system can be modeled on one scale while smaller- and larger-scale behaviors remain unpredictable.
In group theory, a word is any written product of group elements and their inverses. For example, if x, y and z are elements of a group G, then xy, z −1 xzz and y −1 zxx −1 yz −1 are words in the set {x, y, z}. Two different words may evaluate to the same value in G, [1] or even in every group. [2]