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  2. Hypixel - Wikipedia

    en.wikipedia.org/wiki/Hypixel

    Hypixel Network, [3] simply known as Hypixel, is a Minecraft server that hosts minigames. It was released on April 13, 2013 by Simon "hypixel" (name of player is not written like the name of the server, but with a lower h (see list of admins)) Collins-Laflamme and Philippe Touchette, and is managed and run by Hypixel Inc. [4] Hypixel is only available on the Java Edition of Minecraft, [5] but ...

  3. Tier list - Wikipedia

    en.wikipedia.org/wiki/Tier_list

    Tier lists have been used to rank elements from other subjects aside from video games, such as films, sports teams, logos, animals, and tabletop games. [ 2 ] [ failed verification ] Their purpose is usually to give room for discussion in the subject, to create an easily understandable overview, or simply to entertain.

  4. Henley Passport Index - Wikipedia

    en.wikipedia.org/wiki/Henley_Passport_Index

    The Henley Passport index ranks passports according to the number of destinations that can be reached using a particular country's ordinary passport without the need of a prior visa ("visa-free"). [ 9 ] [ 10 ] [ 11 ] The survey ranks 199 passports against 227 destination [ 12 ] countries , territories , and micro-states .

  5. Free group - Wikipedia

    en.wikipedia.org/wiki/Free_group

    A free group of finite rank n > 1 has an exponential growth rate of order 2n − 1. A few other related results are: The Nielsen–Schreier theorem: Every subgroup of a free group is free. Furthermore, if the free group F has rank n and the subgroup H has index e in F, then H is free of rank 1 + e(n–1). A free group of rank k clearly has ...

  6. P-group generation algorithm - Wikipedia

    en.wikipedia.org/wiki/P-group_generation_algorithm

    The last but one quotient of the maximal path of is the elementary abelian p-group () = / of rank = (), where () = ⁡ ((,)) denotes the generator rank of . Generally, the descendant tree T ( G ) {\displaystyle {\mathcal {T}}(G)} of a vertex G {\displaystyle G} is the subtree of all descendants of G {\displaystyle G} , starting at the root G ...

  7. Generator matrix - Wikipedia

    en.wikipedia.org/wiki/Generator_matrix

    A generator matrix for a linear [,,]-code has format , where n is the length of a codeword, k is the number of information bits (the dimension of C as a vector subspace), d is the minimum distance of the code, and q is size of the finite field, that is, the number of symbols in the alphabet (thus, q = 2 indicates a binary code, etc.).

  8. Polish Armed Forces rank insignia - Wikipedia

    en.wikipedia.org/wiki/Polish_Armed_Forces_rank...

    Until 2004 the ranks of chorąży (OR-9 and OR-8) constituted a separate group, roughly corresponding to U.S. Warrant Officers. On July 1, 2004, the number of these ranks was reduced and they were included in the group of non-commissioned ranks.

  9. Rank of an abelian group - Wikipedia

    en.wikipedia.org/wiki/Rank_of_an_abelian_group

    A group is called torsion-free if it has no non-trivial torsion elements. The factor-group A/T(A) is the unique maximal torsion-free quotient of A and its rank coincides with the rank of A. The notion of rank with analogous properties can be defined for modules over any integral domain, the case of abelian groups corresponding to modules over Z.