[GAP Forum] Find a Sylow p-subgroup contains the p-subgroup

[Alexander Hulpke]

Dear Forum, Dear Luyen Le Van,

> Let G be a finite group and p be a prime. Suppose that Q is a p-subgroup of G.
> How to find a Sylow p-subgroup  of G containing Q ?

Compute a p-Sylow subgroup of N_G(Q). It will contain Q, and must be larger. Repeat until the correct order is obtained.

Best,

   Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke