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• Every 1-completed subgroup is contained in a maximal subgroup
  Every 1-completed subgroup is contained in a maximal subgroup. rangle = G. Then, H is contained in a maximal subgroup. ... ...
  666 bytes (110 words) - 23:51, 5 July 2019
• Abelian minimal normal subgroup and core-free maximal subgroup are permutable complements
  Suppose G is a primitive group with core-free maximal subgroup M. ... ===Maximal subgroup=== Maximal subgroup A maximal subgroup of a group ... ...
  3 KB (442 words) - 11:23, 2 January 2009
• Abelian normal subgroup of core-free maximal subgroup is contranormal implies commutator subgroup is monolith
  #REDIRECT Abelian normal subgroup of core-free maximal subgroup is contranormal implies derived subgroup of whole group is monolith ... ...
  135 bytes (18 words) - 20:53, 10 January 2010
• Minimal normal subgroup and core-free maximal subgroup need not be permutable complements
  Suppose G is a primitive group, M is a core-free maximal subgroup of G, and N is a minimal normal subgroup of G. Then, M and N need not be permutable ... ...
  2 KB (322 words) - 05:32, 24 January 2015
• Group where every proper subgroup is contained in a maximal subgroup
  #redirect Group in which every proper subgroup is contained in a maximal subgroup ... ...
  85 bytes (13 words) - 15:17, 13 July 2008
• Group in which every proper subgroup is contained in a maximal subgroup
  A group in which every proper subgroup is contained in a maximal subgroup is a group for which every defining ingredient::proper subgroup (subgroup ... ...
  662 bytes (86 words) - 15:18, 13 July 2008
• Maximal subgroup
  The notion of maximal subgroup probably dates back to the very beginning ... A maximal subgroup of a group is defined in the following equivalent ways: ... ...
  4 KB (533 words) - 22:48, 21 November 2008
• Group in which every subgroup is contained in a maximal subgroup
  #redirect Group in which every proper subgroup is contained in a maximal subgroup ... ...
  85 bytes (13 words) - 18:19, 26 June 2008
• Maximal subgroup of Sylow subgroup
  number. A subgroup H of G is termed a maximal subgroup of p-Sylow subgroup ... * H is a maximal subgroup of some p-Sylow subgroup of G. ... ...
  1 KB (184 words) - 22:47, 4 March 2009
• Characteristic maximal subgroup
  #redirect Characteristic subgroup of prime index ... ...
  52 bytes (6 words) - 20:23, 13 August 2009
• Normal maximal subgroup
  #redirect Normal subgroup of prime index ... ...
  44 bytes (6 words) - 14:27, 22 September 2008
• Group where every maximal subgroup is normal
  #redirect Group in which every maximal subgroup is normal ... ...
  61 bytes (9 words) - 12:12, 29 May 2008
• D8 cyclic maximal subgroup
  #redirect cyclic maximal subgroup of dihedral group:D8 ... ...
  58 bytes (8 words) - 16:10, 22 June 2011
• Abelian normal subgroup of core-free maximal subgroup is contranormal implies derived subgroup of whole group is monolith
  group, M is a core-free maximal subgroup of G (or, the stabilizer ... Given: A group G, a core-free maximal subgroup M of G. An abelian ... ...
  2 KB (353 words) - 19:27, 20 November 2022
• Finite p-group with cyclic maximal subgroup
  A finite p-group with cyclic maximal subgroup is a finite p-group (i.e., a group of prime power order where the underlying prime is p) if it ... ...
  344 bytes (63 words) - 21:44, 9 July 2008
• Cyclic maximal subgroup of dihedral group:D16
  ==Definition== Here, G is the dihedral group:D16, the dihedral group of order sixteen (and hence, degree eight). We use here the presentation: ... ...
  4 KB (608 words) - 00:07, 30 June 2011
• Maximal subgroup in finite nilpotent group
  #REDIRECT Maximal subgroup of finite nilpotent group ... ...
  56 bytes (7 words) - 15:09, 5 August 2009
• Maximal subgroup of finite nilpotent group
  A maximal subgroup in finite nilpotent group is the following equivalent ... * A defining ingredient::maximal subgroup of a defining ingredient::finite ... ...
  1,018 bytes (120 words) - 15:10, 5 August 2009
• Normalizer condition implies every maximal subgroup is normal
  Then, any maximal subgroup of G is a normal subgroup. ==Proof== Given: A group G satisfying the normalizer condition, a maximal subgroup ... ...
  1 KB (186 words) - 01:31, 7 February 2009
• Group in which every maximal subgroup is characteristic
  A group in which every maximal subgroup is characteristic is a group ... * Any defining ingredient::maximal subgroup is a defining ingredient::characteristic ... ...
  1,019 bytes (131 words) - 22:47, 15 September 2009

Page text matches

• Maximal operator
  proper subgroup|maximal subgroup * proper normal subgroup|maximal normal ... by applying this operator are termed maximal subgroup properties. ... ...
  2 KB (283 words) - 23:50, 7 May 2008
• 2-submaximal subgroup
  maximal subgroup|maximal subgroup ==Definition== a 2-submaximal subgroup if it is a maximal subgroup of a maximal subgroup. ... ...
  213 bytes (29 words) - 18:33, 2 December 2008
• Nilpotent implies derived in Frattini
  # Nilpotent implies every maximal subgroup is normal: In a nilpotent ... it suffices to show that any maximal subgroup is normal with Abelian ... ...
  2 KB (288 words) - 18:34, 20 May 2008
• Maximality testing problem
  maximal subgroup ==Description== ===Given data=== Our universe is some group U (such as a linear group or a permutation group) in which products ... ...
  1 KB (211 words) - 23:50, 7 May 2008
• Equivalence of definitions of Frattini subgroup
  * Every 1-completed subgroup is contained in a maximal subgroup ... ===The set of nongenerators is contained in every maximal subgroup=== ... ...
  3 KB (469 words) - 16:57, 25 June 2008
• Group in which every maximal subgroup is normal
  A group in which every maximal subgroup is normal is a group satisfying ... * Any maximal subgroup (i.e. any proper subgroup not contained in ... ...
  2 KB (276 words) - 00:56, 26 December 2015
• Normal subgroup of prime index
  A normal maximal subgroup or normal subgroup of prime index is defined ... group. Nilpotent implies every maximal subgroup is normal ... ...
  1 KB (178 words) - 13:37, 23 September 2008
• Group in which every maximal subgroup is characteristic
  A group in which every maximal subgroup is characteristic is a group ... * Any defining ingredient::maximal subgroup is a defining ingredient::characteristic ... ...
  1,019 bytes (131 words) - 22:47, 15 September 2009
• Modular not implies permutable
  an example of a group with a maximal subgroup that is not permutable. Indeed, in the particular example::symmetric group:S3, the subgroup of ... ...
  510 bytes (69 words) - 13:14, 2 October 2008
• Maximal implies normal or self-normalizing
  Any maximal subgroup of a group is either normal of self-normalizing. ==Related facts== * Maximal implies normal or abnormal * Maximal implies ... ...
  320 bytes (35 words) - 20:57, 21 September 2008
• Maximal implies modular
  Any maximal subgroup of a group is a modular subgroup. ===Statement ... Suppose A is a maximal subgroup of G. Then, if B,C are subgroups of ... ...
  1 KB (213 words) - 13:08, 2 October 2008
• Abelian minimal normal subgroup and core-free maximal subgroup are permutable complements
  Suppose G is a primitive group with core-free maximal subgroup M. ... ===Maximal subgroup=== Maximal subgroup A maximal subgroup of a group ... ...
  3 KB (442 words) - 11:23, 2 January 2009
• Normalizer condition implies every maximal subgroup is normal
  Then, any maximal subgroup of G is a normal subgroup. ==Proof== Given: A group G satisfying the normalizer condition, a maximal subgroup ... ...
  1 KB (186 words) - 01:31, 7 February 2009
• K implies Frattini-free
  any nontrivial element, there is a maximal subgroup not containing that element. ... * Every 1-completed subgroup is contained in a maximal subgroup ... ...
  3 KB (526 words) - 16:16, 25 June 2008
• Cyclic of prime power order iff not generated by proper subgroups
  # It has a unique maximal subgroup, and this subgroup contains every ... if it is not the whole group, it is a maximal subgroup. Moreover, since it ... ...
  2 KB (424 words) - 19:01, 9 November 2008
• GAP:MaximalNormalSubgroups
  a list of all maximal subgroups. Note that a maximal subgroup need not be a maximal normal subgroup and a maximal normal subgroup need not be a maximal ... ...
  1 KB (182 words) - 15:18, 19 August 2009
• Maximal subgroup
  The notion of maximal subgroup probably dates back to the very beginning ... A maximal subgroup of a group is defined in the following equivalent ways: ... ...
  4 KB (533 words) - 22:48, 21 November 2008
• Every 1-completed subgroup is contained in a maximal subgroup
  Every 1-completed subgroup is contained in a maximal subgroup. rangle = G. Then, H is contained in a maximal subgroup. ... ...
  666 bytes (110 words) - 23:51, 5 July 2019
• Maximal subgroup of finite nilpotent group
  A maximal subgroup in finite nilpotent group is the following equivalent ... * A defining ingredient::maximal subgroup of a defining ingredient::finite ... ...
  1,018 bytes (120 words) - 15:10, 5 August 2009
• GAP:MaximalSubgroups
  ==Definition== ===Function type=== MaximalSubgroups is a GAP function that takes as input one argument representing a group and outputs a list ... ...
  1 KB (151 words) - 15:05, 19 August 2009