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• P-constrained and p-stable implies abelian normal subgroup of Sylow subgroup is contained in (p',p)-core
  If H is a normal subgroup of G and Q is a p-Sylow subgroup of H, then HN_G(P) = G. # uses::Sylow satisfies permuting transfer condition ==Proof== ... ...
  4 KB (822 words) - 13:40, 5 August 2009
• Maximal among abelian normal subgroups in p-Sylow subgroup that is not cyclic implies every invariant p'-subgroup is in the p'-core in p-constrained group
  number dividing the order of G. Suppose P is a p-Sylow subgroup and A is maximal among abelian normal subgroups in P (hence, A is a self-centralizing ... ...
  801 bytes (130 words) - 22:52, 12 September 2011

Page text matches

• Equivalence of normality and characteristicity conditions for conjugacy functor
  # For every pair of p-Sylow subgroups P,Q of G, W(P) = W(Q). # For every pair of p-Sylow subgroups P,Q of G, W(P) is a normal subgroup ... ...
  3 KB (570 words) - 19:37, 8 July 2013
• Equivalence of normality and characteristicity conditions for isomorph-free p-functor
  # For every pair of p-Sylow subgroups P,Q of G, W(P) = W(Q). # For every pair of p-Sylow subgroups P,Q of G, W(P) \le Q. ... ...
  4 KB (727 words) - 03:00, 15 January 2012
• Strongly p-solvable implies normalizer of D*-subgroup generates whole group with p'-core for odd p
  # For one (and hence every) p-Sylow subgroup P of G, D^*(P) is a normal ... # For one (and hence every) p-Sylow subgroup P of G, D^*(P) is a characteristic ... ...
  1 KB (224 words) - 19:24, 15 January 2012
• P-constrained and p-stable implies normalizer of D*-subgroup generates whole group with p'-core for odd p
  # For one (and hence every) p-Sylow subgroup P of G, D^*(P) is a normal ... # For one (and hence every) p-Sylow subgroup P of G, D^*(P) is a characteristic ... ...
  2 KB (240 words) - 19:21, 15 January 2012
• Group of Glauberman type for a prime
  # For one (and hence every) p-Sylow subgroup P of G, G = O_{p'} ... # For one (and hence every) p-Sylow subgroup P of G, the image of ... ...
  4 KB (687 words) - 04:33, 15 January 2012
• 2-Sylow subgroup of general linear group:GL(2,3)
  H is one of the 2-Sylow subgroups of G, i.e.: H is isomorphic to semidihedral ... | 2-Sylow subgroups || p-Sylow subgroups are subgroups whose order ... ...
  5 KB (635 words) - 13:37, 28 June 2011
• P-solvable implies p-constrained
  that G is p-solvable. Then, if P is a p-Sylow subgroup, we have: ... * p-constrained not implies p-solvable * The converse is partially ... ...
  4 KB (699 words) - 20:39, 6 December 2011
• Simple-feasible number
  ===Direct facts from Sylow theory=== For a number to be simple-feasible ... * Sylow-unique prime divisor * Core-nontrivial prime divisor ... ...
  2 KB (291 words) - 00:06, 6 January 2009
• P-constrained and p-stable implies Glauberman type for odd p
  # For one (and hence every) p-Sylow subgroup P of G, Z(J(P)) is a ... # For one (and hence every) p-Sylow subgroup P of G, Z(J(P)) is a ... ...
  10 KB (1,701 words) - 19:19, 15 January 2012
• Replacing a subgroup by a normal subgroup
  is called Poincare's theorem, and it implies that if H has finite index ... subgroup, and more generally, of a core-characteristic subgroup, is characteristic ... ...
  6 KB (924 words) - 23:09, 7 November 2011
• Sylow-unique prime divisor
  A prime divisor of a number is said to be Sylow-unique if for every ... A prime divisor p of a number N is said to be Sylow-unique if for ... ...
  3 KB (445 words) - 14:41, 5 January 2009
• Glauberman-Thompson normal p-complement theorem
  and p is an odd prime number. Let P be a p-Sylow subgroup. Then, if N_G(Z ... # uses::Strongly p-solvable implies Glauberman type for odd p: This ... ...
  2 KB (250 words) - 19:51, 15 January 2012
• Sylow subgroup
  A subgroup of a finite group is termed a Sylow subgroup if it is a ... also via Hall), see also Sylow implies core-characteristic || || core ... ...
  16 KB (2,017 words) - 19:02, 20 December 2014
• Maximal among abelian normal subgroups of Sylow subgroup implies direct factor of centralizer
  and p is a prime number. Suppose P is a p-Sylow subgroup of G, and A is fact ... * Hall and central factor implies direct factor * Pi-separable and ... ...
  3 KB (444 words) - 02:10, 17 February 2009
• Lemma on containment in p'-core for Thompson transitivity theorem
  among abelian normal subgroups in a p-Sylow subgroup of G, and A is not ... # uses::Maximal among abelian normal subgroups in p-Sylow subgroup ... ...
  997 bytes (160 words) - 22:54, 12 September 2011
• Order has only two prime factors implies prime divisor with larger prime power is core-nontrivial except in finitely many cases
  of cases. In other words, the p-fact about::Sylow-core of G is nontrivial; ... * Order has only two prime factors implies solvable ==References== ... ...
  1 KB (168 words) - 00:57, 24 February 2011
• Klein four-subgroup of alternating group:A5
  | Sylow subgroup for the prime p = 2 || A p-Sylow subgroup is a subgroup ... The subgroup is a 2-Sylow subgroup, so many properties follow as a ... ...
  6 KB (720 words) - 16:16, 27 June 2011
• Glauberman-Solomon normal p-complement theorem
  and p is an odd prime number. Let P be a p-Sylow subgroup of G. Denote by ... # uses::Strongly p-solvable implies normalizer of D*-subgroup generates ... ...
  1 KB (169 words) - 19:56, 15 January 2012
• A3 in S5
  | Sylow subgroup for the prime p = 3 || A p-Sylow subgroup is a subgroup whose order is a power of p and index is relatively prime to p. Sylow ... ...
  3 KB (417 words) - 16:29, 27 June 2011
• P-constrained group
  is true for one (and hence, any) p-Sylow subgroup of G: ... | Weaker than::p-solvable group || || p-solvable implies p-constrained ... ...
  3 KB (516 words) - 22:18, 6 December 2011