Sylow theorems

Let G be a finite groupMathworldPlanetmath whose order is divisible by the prime p. Suppose pm is the highest power of p which is a factor of |G| and set



  1. 1.

    the group G contains at least one subgroupMathworldPlanetmathPlanetmath of order pm,

  2. 2.

    any two subgroups of G of order pm are conjugatePlanetmathPlanetmath, and

  3. 3.

    the number of subgroups of G of order pm is congruentMathworldPlanetmath to 1 modulo p and is a factor of k.

Title Sylow theoremsMathworldPlanetmath
Canonical name SylowTheorems
Date of creation 2013-03-22 12:24:12
Last modified on 2013-03-22 12:24:12
Owner yark (2760)
Last modified by yark (2760)
Numerical id 6
Author yark (2760)
Entry type Theorem
Classification msc 20D20
Related topic SylowPSubgroup
Related topic ApplicationOfSylowsTheoremsToGroupsOfOrderPq
Related topic SylowsFirstTheorem
Related topic SylowsThirdTheorem
Related topic SylowPSubgroups