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• Group where every finite subgroup is cyclic
  #redirect Group in which every finite subgroup is cyclic ... ...
  60 bytes (9 words) - 12:19, 26 July 2008
• 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
• Subgroup of finite cyclic group
  A subgroup of a group is termed a subgroup of finite cyclic group ... * Stronger than::Variety-containing subgroup of finite group ... ...
  1 KB (126 words) - 02:15, 13 August 2009
• Group in which every finite subgroup is cyclic
  A group in which every finite subgroup is cyclic is a group where ... finite subgroup|finite cyclic subgroup ... ...
  3 KB (457 words) - 22:22, 11 April 2017
• Cyclic normal subgroup of finite group
  A cyclic normal subgroup of finite group is a cyclic normal subgroup ... * Stronger than::Cyclic normal subgroup * Stronger than::Abelian normal ... ...
  902 bytes (100 words) - 21:55, 19 October 2009
• Finite and every subgroup is characteristic implies cyclic
  #redirect Finite group implies cyclic iff every subgroup is characteristic ... ...
  78 bytes (10 words) - 00:18, 22 January 2010
• Classification of finite p-groups with cyclic normal self-centralizing subgroup
  ==References== ===Textbook references=== * Gorenstein , Page 197-198, Lemma 4.8 (Section 5.4) ... ...
  112 bytes (9 words) - 21:29, 13 July 2008
• Classification of finite p-groups with self-centralizing cyclic normal subgroup
  A finite p-group (a group of prime power order) P, with a self-centralizing ... * If p is an odd prime, it is a faithful semidirect product of cyclic ... ...
  685 bytes (99 words) - 21:02, 16 September 2008
• Group in which every finite abelian subgroup is cyclic
  A group in which every finite abelian subgroup is cyclic is a group ... finite abelian subgroup|finite cyclic subgroup ==Relation with other ... ...
  1 KB (152 words) - 15:56, 11 April 2017
• Finite group implies cyclic iff every subgroup is characteristic
  The following are equivalent for a fact about::finite group: # It is a fact about::cyclic group, i.e., a finite cyclic group. ... ...
  882 bytes (121 words) - 00:21, 22 January 2010
• Finite group in which every nilpotent subgroup is cyclic
  #redirect Z-group ... ...
  21 bytes (2 words) - 01:47, 11 February 2010
• Finite group in which every abelian subgroup is cyclic
  #redirect finite group with periodic cohomology ... ...
  51 bytes (6 words) - 20:04, 12 January 2013
• Classification of finite p-groups with cyclic maximal subgroup
  This page classifies all finite p-groups that possess a cyclic maximal subgroup. ==Statement== ===For odd primes=== Let p be an odd prime, and ... ...
  15 KB (2,590 words) - 19:36, 25 July 2009
• Multiplicative group of a field implies every finite subgroup is cyclic
  The multiplicative group of a field is a group in which every finite ... ===For finite fields=== * Multiplicative group of a prime field is cyclic ... ...
  1 KB (184 words) - 15:42, 9 February 2009
• Cyclic subgroup of maximum order is direct factor in finite abelian group
  Suppose G is a finite abelian group and H is a cyclic subgroup of G such that the order of H is greater than or equal to the order of any cyclic ... ...
  575 bytes (99 words) - 21:54, 12 January 2013
• At most n elements of order dividing n implies every finite subgroup is cyclic
  property of being a group in which every finite subgroup is cyclic. ... x \in G satisfying x^n = 1. Then, every finite subgroup of G is cyclic. ... ...
  4 KB (792 words) - 05:06, 27 December 2021

Page text matches

• Cyclicity is subgroup-closed
  Every subgroup of a cyclic group is cyclic. ==Facts used== # Every nontrivial subgroup of the group of integers is cyclic on ... ...
  2 KB (282 words) - 20:51, 8 September 2008
• Three-step group
  A finite group G is said to be a three-step group if it satisfies ... * The commutator subgroup G' has a permutable complement Q which ... ...
  769 bytes (131 words) - 00:26, 8 May 2008
• Classification of finite p-groups of rank one
  Let p be a prime, and let P be a finite p-group (a group whose order ... # If p is odd, then P must be cyclic # If p = 2, then P is either cyclic ... ...
  2 KB (290 words) - 19:23, 6 October 2008
• Group in which every finite abelian subgroup is cyclic
  A group in which every finite abelian subgroup is cyclic is a group ... finite abelian subgroup|finite cyclic subgroup ==Relation with other ... ...
  1 KB (152 words) - 15:56, 11 April 2017
• Subgroup of finite cyclic group
  A subgroup of a group is termed a subgroup of finite cyclic group ... * Stronger than::Variety-containing subgroup of finite group ... ...
  1 KB (126 words) - 02:15, 13 August 2009
• 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
• Classification of metacyclic p-groups
  This page classifies all finite p-groups that are metacyclic: there is a cyclic normal subgroup with a cyclic quotient group. ==Related facts== ... ...
  941 bytes (140 words) - 16:18, 16 September 2008
• Finitely many subgroups iff finite
  * The group is a fact about::finite group, i.e., its order (the number ... # uses::Every group is a union of cyclic subgroups ==Proof== ... ...
  2 KB (260 words) - 16:08, 31 October 2008
• Cyclic implies every subgroup is characteristic
  In a cyclic group, every subgroup is a characteristic subgroup. ... * Cyclic implies every subgroup is quotient-isomorph-free ... ...
  453 bytes (52 words) - 00:16, 22 January 2010
• Classification of finite p-groups of normal rank one
  Suppose P is a finite p-group whose normal rank is one: every Abelian ... * If p is odd, P is itself cyclic. * If p = 2, P is either cyclic, ... ...
  4 KB (734 words) - 19:17, 6 October 2008
• Multiplicative group of a field implies every finite subgroup is cyclic
  The multiplicative group of a field is a group in which every finite ... ===For finite fields=== * Multiplicative group of a prime field is cyclic ... ...
  1 KB (184 words) - 15:42, 9 February 2009
• Classification of finite p-groups with self-centralizing cyclic normal subgroup
  A finite p-group (a group of prime power order) P, with a self-centralizing ... * If p is an odd prime, it is a faithful semidirect product of cyclic ... ...
  685 bytes (99 words) - 21:02, 16 September 2008
• Structure theorem for fixed point-free automorphism group of p-group
  Suppose P is a group of prime power order, i.e., a finite p-group ... # Every Abelian subgroup of G is cyclic. # If q and r are primes dividing ... ...
  1 KB (216 words) - 23:05, 7 October 2008
• Finite group implies cyclic iff every subgroup is characteristic
  The following are equivalent for a fact about::finite group: # It is a fact about::cyclic group, i.e., a finite cyclic group. ... ...
  882 bytes (121 words) - 00:21, 22 January 2010
• Cyclic automorphism group not implies cyclic
  is an [group whose automorphism group is cyclic]] (i.e., the automorphism ... * Finite and cyclic automorphism group implies cyclic * Cyclic automorphism ... ...
  1 KB (226 words) - 16:53, 25 June 2013
• Cyclic normal subgroup of finite group
  A cyclic normal subgroup of finite group is a cyclic normal subgroup ... * Stronger than::Cyclic normal subgroup * Stronger than::Abelian normal ... ...
  902 bytes (100 words) - 21:55, 19 October 2009
• Cyclic normal implies potentially verbal in finite
  Suppose K is a finite group and H is a cyclic normal subgroup of K ... * Cyclic normal implies finite-pi-potentially verbal in finite ... ...
  1 KB (178 words) - 14:38, 20 October 2009
• Finite-potentially verbal subgroup
  A subgroup H of a finite group K is termed a finite-potentially verbal ... * Weaker than::Central subgroup of finite group: Central implies potentially ... ...
  765 bytes (99 words) - 21:13, 19 October 2009
• Cyclic of prime power order iff not generated by proper subgroups
  # It has a unique maximal subgroup, and this subgroup contains every ... # It is a cyclic group whose order is a power of a prime. ... ...
  2 KB (424 words) - 19:01, 9 November 2008
• Group in which every finite subgroup is cyclic
  A group in which every finite subgroup is cyclic is a group where ... finite subgroup|finite cyclic subgroup ... ...
  3 KB (457 words) - 22:22, 11 April 2017