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• Coprime automorphism-invariant normal subgroup of Hall subgroup is normalizer-relatively normal
  about::coprime automorphism-invariant normal subgroup of G. Then, H is normal ... of G, a coprime automorphism-invariant normal subgroup H of K. ... ...
  2 KB (261 words) - 18:57, 9 March 2009
• Center is normality-large implies every nontrivial normal subgroup contains a cyclic normal subgroup
  a group in which every nontrivial normal subgroup contains a cyclic normal ... its intersection with every nontrivial normal subgroup is nontrivial, then ... ...
  537 bytes (72 words) - 15:55, 13 July 2008
• Supersolvable implies every nontrivial normal subgroup contains a cyclic normal subgroup
  a group in which every nontrivial normal subgroup contains a cyclic normal ... Let G be a supersolvable group. Then, if N is a nontrivial normal ... ...
  2 KB (292 words) - 14:42, 18 July 2008
• Nilpotent implies every nontrivial normal subgroup contains a cyclic normal subgroup
  In a nilpotent group, every nontrivial normal subgroup contains a ... # uses::Center is normality-large implies every nontrivial normal ... ...
  465 bytes (56 words) - 20:13, 21 September 2008
• Normal subgroup of normal subgroup need not be normal
  #redirect normality is not transitive ... ...
  41 bytes (5 words) - 18:03, 26 February 2011
• No nontrivial abelian normal p-subgroup for some prime p implies every normal subgroup is strongly image-potentially characteristic
  is a power of p). Suppose H is a normal subgroup. Then, H is a strongly ... some prime p implies every p-divisible normal subgroup is potentially characteristic ... ...
  3 KB (595 words) - 14:31, 30 May 2009
• Supersolvable implies every normal subgroup contains a cyclic normal subgroup
  #REDIRECT Supersolvable implies every nontrivial normal subgroup contains a cyclic normal subgroup ... ...
  102 bytes (12 words) - 19:47, 7 July 2008
• Group in which every nontrivial normal subgroup contains a cyclic normal subgroup
  A group in which every nontrivial normal subgroup contains a cyclic ... Nilpotent implies every nontrivial normal subgroup contains a cyclic normal ... ...
  2 KB (284 words) - 20:12, 21 September 2008
• Group in which every nontrivial normal subgroup contains a minimal normal subgroup
  A group in which every nontrivial normal subgroup contains a minimal normal subgroup is a group with the property that any nontrivial normal ... ...
  452 bytes (58 words) - 18:25, 13 July 2008
• No nontrivial abelian normal p-subgroup for some prime p implies every p-divisible normal subgroup is potentially characteristic
  p-subgroup. Suppose H is a p-divisible normal subgroup of G: in other words ... * No nontrivial abelian normal p-subgroup implies every normal subgroup ... ...
  4 KB (672 words) - 14:49, 30 May 2009
• Closed normal subgroup for Lie structure need not be closed normal subgroup of algebraic group
  or field of complex numbers), and a normal subgroup H of G such that H is ... * H is a discrete closed normal subgroup of G with the Lie group topology ... ...
  2 KB (399 words) - 01:02, 2 January 2012
• Join lemma for normal subgroup of subgroup with normal subgroup of whole group
  * Join of subnormal subgroup and normal subgroup is subnormal ==Proof== ... ...
  437 bytes (55 words) - 03:30, 30 December 2010
• Any class two normal subgroup whose derived subgroup is in the ZJ-subgroup normalizes an abelian subgroup of maximum order
  a finite p-group, and B is a class two normal subgroup of P such that its commutator ... * Any abelian normal subgroup normalizes an abelian subgroup of maximum ... ...
  2 KB (340 words) - 20:51, 10 January 2010
• Any class two normal subgroup whose commutator subgroup is in the ZJ-subgroup normalizes an abelian subgroup of maximum order
  #REDIRECT Any class two normal subgroup whose derived subgroup is in the ZJ-subgroup normalizes an abelian subgroup of maximum order ... ...
  136 bytes (20 words) - 20:51, 10 January 2010
• Commutator of a normal subgroup and a subgroup not implies normal
  It is possible to have a group L, a fact about::normal subgroup K ... * Commutator of a normal subgroup and a subset implies 2-subnormal: ... ...
  4 KB (701 words) - 19:09, 19 January 2009
• Normal subgroup of complemented normal subgroup
  A subgroup H of a group G is termed a normal subgroup of complemented ... * Weaker than::Direct factor of complemented normal subgroup ... ...
  864 bytes (120 words) - 22:05, 17 May 2009
• Transitively normal subgroup of normal subgroup
  A subgroup H of a group G is termed a transitively normal subgroup ... * Weaker than::Normal subgroup * Weaker than::Direct factor of normal ... ...
  848 bytes (117 words) - 21:41, 20 May 2009
• Question:Normal subgroup of normal subgroup big deal
  Q: I was told that it is very important and counter-intuitive that a normal subgroup of a normal subgroup need not be normal, but I didn't ... ...
  2 KB (313 words) - 22:55, 1 April 2011
• Normal subgroup comparable with all normal subgroups implies characteristic in finite
  #REDIRECT Normal subgroup comparable with all normal subgroups implies characteristic in finite group ... ...
  105 bytes (13 words) - 21:46, 12 August 2013
• Commutator of transitively normal subgroup and subset implies normal
  #redirect Commutator of a transitively normal subgroup and a subset implies normal ... ...
  86 bytes (12 words) - 17:50, 20 July 2009

Page text matches

• Normal
  * Normal subgroup * Normal automorphism * Normal core * Normal closure * Normalizer * Normal topological group Alternatively search for normal ... ...
  314 bytes (40 words) - 18:14, 22 May 2008
• Frattini-embedded normal in subgroup and normal implies Frattini-embedded normal
  * H is a normal subgroup of G * H is a Frattini-embedded normal subgroup of K. In other words, H ... ...
  3 KB (441 words) - 23:31, 7 May 2008
• Every subgroup is contracharacteristic in its normal closure
  as a contracharacteristic subgroup of a normal subgroup. ... * Equivalence of definitions of subgroup of Abelian normal subgroup ... ...
  1 KB (231 words) - 21:13, 24 October 2008
• Frattini-embedded normal-realizable implies inner-in-automorphism-Frattini
  in some group H as a Frattini-embedded normal subgroup. Then G satisfies the ... The inner automorphism group of G is a Frattini-embedded normal subgroup ... ...
  2 KB (262 words) - 23:31, 7 May 2008
• Cyclic normal implies hereditarily normal
  Any subgroup of a cyclic normal subgroup is normal. (Also, any subgroup ... The subgroup property of being a cyclic normal subgroup is stronger ... ...
  1 KB (207 words) - 10:41, 8 August 2008
• Normality-large normal subgroup
  A normality-large normal subgroup is a subgroup that satisfies the ... # Its intersection with every nontrivial normal subgroup is a nontrivial ... ...
  810 bytes (96 words) - 18:16, 13 July 2008
• Center of normal implies normal
  The center of any normal subgroup, is a normal subgroup of the whole group. ... if there is a nontrivial nilpotent normal subgroup, there is a nontrivial ... ...
  934 bytes (130 words) - 23:13, 7 May 2008
• No proper nontrivial transitively normal subgroup not implies simple
  but has no proper nontrivial transitively normal subgroup. ... ===Transitively normal subgroup=== Transitively normal subgroup ... ...
  2 KB (334 words) - 20:03, 14 October 2008
• Normality-large and minimal normal implies monolith
  A fact about::minimal normal subgroup of a group that is normality ... Given: A group G, a minimal normal subgroup N such that if N \cap ... ...
  1 KB (189 words) - 20:38, 30 August 2008
• Intermediately normal-to-characteristic implies intermediately characteristic in nilpotent
  G if whenever H \le K \le G, with H a normal subgroup of K, H is a characteristic ... ===Intermediately subnormal-to-normal subgroup=== Intermediately subnormal ... ...
  3 KB (360 words) - 11:00, 19 September 2008
• Question:Normal subgroup product with subgroups
  Q: The product of a normal subgroup with any subgroup is a subgroup. Are normal subgroups the only subgroups with this property? A: No. A subgroup ... ...
  926 bytes (129 words) - 22:54, 1 April 2011
• Normal-homomorph-containing implies strictly characteristic
  image condition: The image of a normal subgroup under a surjective homomorphism ... Given: A normal subgroup N of a group G such that whenever \varphi:N ... ...
  2 KB (319 words) - 20:44, 2 December 2008
• Question:Normal subgroup characteristic in bigger group
  Q: Suppose H is a normal subgroup of a group G. Is it always possible to find a group K containing G such that H is a characteristic subgroup of K? ... ...
  1 KB (174 words) - 03:30, 30 July 2013
• Subnormal not implies normal
  weaker = normal subgroup}} ==Statement== A subnormal subgroup of a ... normality is not transitive, i.e. a normal subgroup of a normal subgroup ... ...
  503 bytes (71 words) - 10:39, 8 August 2008
• Composition of subgroup property satisfying intermediate subgroup condition with normality equals property in normal closure
  with property p of a fact about::normal subgroup. H has the property ... | Normal subgroup || 2-subnormal subgroup || Normality satisfies intermediate ... ...
  2 KB (256 words) - 11:58, 17 September 2008
• Questions:Normal subgroup
  This is a questions page on normal subgroup, listing common questions that may occur both to people encountering the definition for the first ... ...
  932 bytes (125 words) - 16:19, 3 August 2011
• Applying characteristic of normal implies normal
  normal: any characteristic subgroup of a normal subgroup is normal in the whole group. ... ...
  299 bytes (39 words) - 20:16, 16 October 2008
• Hall subgroup of normal subgroup
  A subgroup of a finite group is termed a Hall subgroup of normal subgroup ... * Weaker than::Intersection of Hall subgroup and normal subgroup ... ...
  636 bytes (74 words) - 21:18, 29 September 2008
• Sylow subgroup of normal subgroup
  A subgroup of a finite group is termed a Sylow subgroup of normal ... # It is a Sylow subgroup of a normal subgroup of the whole group. ... ...
  1 KB (130 words) - 20:53, 1 November 2008
• Subnormal-to-normal is normalizer-closed
  Suppose H is a subnormal-to-normal subgroup of a group G: either H ... Given: A subnormal-to-normal subgroup H of a group G, with normalizer ... ...
  2 KB (249 words) - 19:47, 8 October 2008