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  • The Group Properties Wiki is designed and organized using a property-theoretic paradigm. This ar Examples from group theory:
    7 KB (1,067 words) - 22:24, 7 May 2008
  • ...ties over structures and the algebraic and logical relations between those properties'' Examples from group theory:
    4 KB (575 words) - 22:44, 7 May 2008
  • This is an informal account of the story of the development of the Group Properties Wiki, till 2007. The '''Group Properties Wiki''', called ''groupprops'' first began life at
    2 KB (398 words) - 22:44, 7 May 2008
  • ...lves whatever problem we are considering in terms of oracle queries to the group operations and any pre-processing or post-processing that needs to be done. Any black-box group algorithm gives an actual algorithm if we are actually provided an encoding
    2 KB (408 words) - 07:21, 21 December 2014
  • ...nsion <math>F</math> over <math>\mathbb{Q}</math> satisfying the following properties. Let <math>I</math> denote the ring of algebraic integers in <math>F</math>
    2 KB (401 words) - 23:12, 7 May 2008
  • An element of a [[group]] is termed central if the following equivalent conditions hold: # It commutes with every element of the group
    15 KB (2,081 words) - 20:14, 1 June 2016
  • Let <math>\sigma</math> be an automorphism of a group <math>G</math>. We say that <math>\sigma</math> is '''characteristic-semidi ===Stronger properties===
    1 KB (150 words) - 15:44, 8 April 2009
  • A [[subgroup]] of a [[group]] is termed a '''characteristic direct factor''' if it is a [[characteristi * Every group is a characteristic direct factor of itself.
    4 KB (455 words) - 02:59, 20 January 2013
  • ...core]] is a [[defining ingredient::characteristic subgroup]] of the whole group. A [[subgroup]] <math>H</math> of a [[group]] <math>G</math> is termed '''core-characteristic''' if the normal core <ma
    3 KB (285 words) - 17:34, 21 December 2014
  • A prime divisor of a number is said to be '''core-nontrivial''' if for every group whose order is that number, the core for that prime divisor is nontrivial. ...nontrivial''' if for any group <math>G</math> of order <math>N</math>, the group <math>O_p(G)</math> (viz the <math>p</math>-core of <math>G</math>) is nont
    2 KB (413 words) - 23:24, 7 May 2008
  • {{prime-parametrized sdf}} Let <math>G</math> be a [[finite group]] of order <math>N</math> and let <math>p</math> be a prime divisor of <mat
    2 KB (287 words) - 23:24, 7 May 2008
  • A family <math>\mathcal{F}</math> of subgroups of a group <math>G</math> is termed a '''cover''' for <math>G</math> if it satisfies t ==Properties==
    876 bytes (150 words) - 23:24, 7 May 2008
  • {{nottobeconfusedwith|[[critical group]]}} ...bgroup''' if it is [[characteristic subgroup|characteristic]] in the whole group and satisfies the following three conditions:
    4 KB (489 words) - 00:05, 13 February 2009
  • {{pivotal group property}} {{natural number-parametrized group family}}
    8 KB (1,111 words) - 23:25, 20 June 2013
  • {{particular group}} ...ined as the unique group of order two. Explicitly it can be described as a group with two elements, say <math>e</math> and <math>x</math> such that <math>ex
    8 KB (1,234 words) - 05:31, 21 January 2013
  • {{particular group}} ...ined as the unique group of order 3. Equivalently it can be described as a group with three elements <math>e= x^0,x,x^2</math> where <math>x^lx^m = x^{l+m}<
    6 KB (839 words) - 04:07, 12 January 2013
  • {{prime set-parametrized group property}} Let <math>G</math> be a [[finite group]], and <math>\pi</math> be a set of primes. We say that <math>G</math> sati
    821 bytes (134 words) - 23:25, 7 May 2008
  • {{nottobeconfusedwith|[[dicyclic group]] (also called binary dihedral group)}} {{group property}}
    10 KB (1,448 words) - 02:22, 6 July 2019
  • {{particular group}} ...times the ''octic group'', is defined by the following [[presentation of a group|presentation]], with <math>e</math> denoting the identity element:
    19 KB (2,660 words) - 13:15, 14 February 2015
  • ...up correlates with the way the normal subgroups are distributed within the group? This, and other related questions, are explored within this article. ! Group !! Order !! Orders of normal subgroups (with multiplicity) !! Indexes of no
    11 KB (1,600 words) - 23:24, 3 November 2010

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