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• Commutator of normal subgroups equals normal closure of commutators of generators
  K. Then, the commutator subgroup [H,K] is the normal closure of the subgroup: \langle [a,b] \mid a \in A, b \in B \rangle In other words, it is ... ...
  534 bytes (98 words) - 20:14, 1 July 2008
• Subgroup whose normal closure equals its normal core of normalizer
  #redirect subgroup with unique 2-subnormal series ... ...
  53 bytes (6 words) - 14:51, 11 January 2010
• Normal closure
  The normal closure of a subgroup in a group can be defined in any ... Normal closure is also used for normal closure of a subset which is ... ...
  4 KB (629 words) - 19:29, 29 April 2010
• Normal closure-finding
  #redirect Normal closure-finding problem ... ...
  44 bytes (4 words) - 23:52, 7 May 2008
• Normal closure-finding problem
  The normal closure-finding problem is the general name for a class ... * Normality testing problem: See black-box reduction of normal closure ... ...
  637 bytes (90 words) - 20:48, 25 June 2013
• Every subgroup is contracharacteristic in its normal closure
  a contracharacteristic subgroup of its normal closure. In particular, it occurs ... Given: A subgroup H \le G, H^G is the normal closure of H in G. ... ...
  1 KB (231 words) - 21:13, 24 October 2008
• Subgroup whose normal closure is homomorph-containing
  A subgroup H of a group G is termed a subgroup whose normal closure ... its conjugates || || || subgroup whose normal closure is homomorph-containing ... ...
  3 KB (339 words) - 07:07, 21 December 2014
• Subgroup whose normal closure is characteristic
  #redirect closure-characteristic subgroup ... ...
  45 bytes (3 words) - 23:32, 11 January 2010
• Subgroup whose normal closure equals its normalizer
  #redirect subgroup whose normalizer equals its normal closure ... ...
  65 bytes (8 words) - 14:50, 11 January 2010
• Subgroup whose normaliser equals its normal closure
  #redirect subgroup whose normalizer equals its normal closure ... ...
  65 bytes (8 words) - 14:49, 11 January 2010
• Subgroup whose normalizer equals its normal closure
  a subgroup whose normalizer equals its normal closure if it satisfies the following ... H in G equals the defining ingredient::normal closure H^G of H in G. ... ...
  2 KB (204 words) - 14:44, 11 January 2010
• Normal closure of finite subset
  A subgroup of a group is termed a normal closure of finite subset if there is a finite subset of that subgroup such that the normal subgroup ... ...
  788 bytes (106 words) - 20:41, 27 April 2010
• Normal closure-closed subgroup property
  A subgroup property is said to be normal closure-closed if whenever ... ==Subgroup properties that are normal closure-closed== ===Join-closed ... ...
  2 KB (244 words) - 23:52, 7 May 2008
• Subgroup whose normal closure is fully invariant
  A subgroup H of a group G is termed a subgroup whose normal closure ... endomorphisms || || || subgroup whose normal closure is fully invariant|fully ... ...
  4 KB (521 words) - 07:14, 21 December 2014
• Group that is the normal closure of a singleton subset
  A group G is termed a group that is the normal closure of a singleton ... equivalently, the defining ingredient::normal closure of the subgroup it generates ... ...
  2 KB (198 words) - 20:56, 27 April 2010
• Normal closure of 2-subnormal subgroup of prime order is abelian
  prime number p. Then, the fact about::normal closure of H in G is an abelian group. ... * Normal closure of 2-subnormal subgroup of prime power order in nilpotent ... ...
  684 bytes (107 words) - 14:22, 11 September 2011
• Normal closure of 2-subnormal subgroup of prime order in nilpotent group is abelian
  prime number p. Then, the fact about::normal closure of H in G is an abelian group. ... * Weaker than::Normal closure of 2-subnormal subgroup of prime order ... ...
  864 bytes (131 words) - 14:21, 11 September 2011
• Normal closure of 3-subnormal subgroup of prime order in nilpotent group need not be abelian
  number p such that the fact about::normal closure H^G of H in G is not ... * Normal closure of 2-subnormal subgroup of prime order in nilpotent ... ...
  1 KB (234 words) - 14:33, 11 September 2011
• Composition of subgroup property satisfying intermediate subgroup condition with normality equals property in normal closure
  property p inside the fact about::normal closure. In other words, H has this property in G if H satisfies property p as a subgroup of its normal ... ...
  2 KB (256 words) - 11:58, 17 September 2008
• Normal closure of 2-subnormal subgroup of prime power order in nilpotent group has nilpotency class at most equal to prime-base logarithm of order
  prime number p. Then, the fact about::normal closure H^G of H in G is a nilpotent ... * Normal closure of 2-subnormal subgroup of prime order in nilpotent ... ...
  3 KB (538 words) - 22:00, 10 September 2011

Page text matches

• Normal closure-closed subgroup property
  A subgroup property is said to be normal closure-closed if whenever ... ==Subgroup properties that are normal closure-closed== ===Join-closed ... ...
  2 KB (244 words) - 23:52, 7 May 2008
• Commutator of two subgroups
  ===Normal closure and quotient=== in general, be a normal subgroup. The normal closure of the commutator of ... ...
  3 KB (609 words) - 22:08, 22 October 2008
• Sylow-closure
  a Sylow-closure if it occurs as the normal closure of a Sylow subgroup. In the prime parametrized sense, the p-Sylow closure is the normal ... ...
  409 bytes (61 words) - 00:24, 8 May 2008
• Three subgroup lemma
  ===Any one contained in normal closure of subgroup generated by other ... Further, A,B],C] is contained in the [[normal closure of the subgroup ... ...
  2 KB (350 words) - 13:53, 7 July 2008
• Normal closure
  The normal closure of a subgroup in a group can be defined in any ... Normal closure is also used for normal closure of a subset which is ... ...
  4 KB (629 words) - 19:29, 29 April 2010
• Every subgroup is contracharacteristic in its normal closure
  a contracharacteristic subgroup of its normal closure. In particular, it occurs ... Given: A subgroup H \le G, H^G is the normal closure of H in G. ... ...
  1 KB (231 words) - 21:13, 24 October 2008
• Subgroup whose normal closure is homomorph-containing
  A subgroup H of a group G is termed a subgroup whose normal closure ... its conjugates || || || subgroup whose normal closure is homomorph-containing ... ...
  3 KB (339 words) - 07:07, 21 December 2014
• Normal
  * Normal closure * Normalizer * Normal topological group Alternatively search for normal using our search feature or Google for it on this wiki. ... ...
  314 bytes (40 words) - 18:14, 22 May 2008
• Subgroup whose characteristic closure is fully invariant
  | Weaker than::subgroup whose normal closure is fully invariant || || since characteristic implies normal and fully invariant implies characteristic ... ...
  1 KB (154 words) - 06:40, 21 December 2014
• Characteristic closure
  * Normal closure * Characteristic core * Normal core ===Normal closure operator=== The fact that characteristicity is the ... ...
  3 KB (477 words) - 00:51, 12 January 2010
• 2-subnormality is not finite-join-closed
  descending subnormal series: the normal closure of H in G is H_2, and ... P is 2-subnormal, because the normal closure of P, defined as Q = ... ...
  4 KB (635 words) - 23:57, 26 November 2008
• Group that is the characteristic closure of a singleton subset
  | Weaker than::Group that is the normal closure of a singleton subset || normal closure of a singleton subset || || || group that is the characteristic ... ...
  2 KB (297 words) - 00:39, 12 January 2010
• Normal closure-finding problem
  The normal closure-finding problem is the general name for a class ... * Normality testing problem: See black-box reduction of normal closure ... ...
  637 bytes (90 words) - 20:48, 25 June 2013
• Subgroup whose normalizer equals its normal closure
  a subgroup whose normalizer equals its normal closure if it satisfies the following ... H in G equals the defining ingredient::normal closure H^G of H in G. ... ...
  2 KB (204 words) - 14:44, 11 January 2010
• Normal closure of 2-subnormal subgroup of prime order is abelian
  prime number p. Then, the fact about::normal closure of H in G is an abelian group. ... * Normal closure of 2-subnormal subgroup of prime power order in nilpotent ... ...
  684 bytes (107 words) - 14:22, 11 September 2011
• Subgroup whose normal closure is fully invariant
  A subgroup H of a group G is termed a subgroup whose normal closure ... endomorphisms || || || subgroup whose normal closure is fully invariant|fully ... ...
  4 KB (521 words) - 07:14, 21 December 2014
• Normal closure of 2-subnormal subgroup of prime order in nilpotent group is abelian
  prime number p. Then, the fact about::normal closure of H in G is an abelian group. ... * Weaker than::Normal closure of 2-subnormal subgroup of prime order ... ...
  864 bytes (131 words) - 14:21, 11 September 2011
• 2-subnormality is strongly intersection-closed
  Proof: Let K_i be the normal closure of H_i in G. Thus, each K_i is ... (Note that K is not necessarily the normal closure of H in G -- we ... ...
  2 KB (320 words) - 21:16, 17 October 2008
• Normal closure-finding
  #redirect Normal closure-finding problem ... ...
  44 bytes (4 words) - 23:52, 7 May 2008
• Subgroup whose normaliser equals its normal closure
  #redirect subgroup whose normalizer equals its normal closure ... ...
  65 bytes (8 words) - 14:49, 11 January 2010