Sylow theorem

Related BrainMass Solutions

• Sylow's Theorem

  90970 Sylow's Theorem Group Theory Modern Algebra Group Theory (CX) Sylow's Theorem Find all 3-Sylow subgroups

• Sylow's Theorem

  Modern Algebra Group Theory (CIX) Sylow's Theorem In the symmetric group of degree 4, S4 , find a 2-Sylow subgroup and a 3-Sylow subgroup.

• Sylow Theorem Examined

  So G has unique Sylow q-subgroup. Still according to the Sylow Theorem, the Sylow q-subgroup is normal in G. Therefore, G is not simple. Sylow Theorem is contextualized.

• Sylow p-Subgroups, Conjugacy and Abelian Groups

  Suppose is a Sylow-p subgroup of , then is a p-subgroup of . According to the second Sylow Theorem, must be subgroup of a Sylow-p subgroup of .

• Sylow's Theorem

  According to Sylow's Theorem, the number of its Sylow 5-subgroup is 5k+1 | 2^3 = 8. Then the only possibility is k = 0. So G has unique Sylow 5-subgroup and hence it must be normal.

• Proof that There Are No Simple Groups of Order 56 or 148

  Now G can only be simple if it has 7 Sylow-2 subgroups and 8 Sylow-7 subgroups. We know from Sylow's second theorem that all Sylow-p subgroups are conjugate. In particular, all eight Sylow-7 subgroups must be conjugate.

• Sylow's Theorem Problems

  This solution explains how to solve problems related to Sylow's theorem.

• Groups : Third Sylow Theorem

  Permutations are found using the third Sylow theorem. The solution is detailed and well presented.

• Abstract Algebra : Abelian Groups, Cauchy's Theorem, LaGrange's Theorem and Sylow Subgroups

  Abelian Groups, Cauchy's Theorem, LaGrange's Theorem and Sylow Subgroups are investigated.