Let G be a group of order 48. By the 1st Sylow theorem G has a Sylow 2-subgroup and a Sylow 3-subgroup. Suppose none of these are normal. Determine the number of Sylow 2-subgroups and Sylow 3-subgroups that G can have. Justify your answer.© BrainMass Inc. brainmass.com March 4, 2021, 10:46 pm ad1c9bdddf
We note that |G| = 48 = 2^4 * 3
If m is the number of Sylow 2-subgroups that G may have, then m = 1 (mod 2). So m = 2k+1. We also have m|3, then ...
Determine the number of Sylow 2-subgroups and Sylow 3-subgroups that group G can have.