Past exam of the mathematics course of the University of Cambridge / 2018 / ib / Paper 1 / 10G / a

Table of contents
- Solution a

Solution

Write

∣ G ∣ = p^{n} m

with

p ∤ m

. The Sylow theorems state:

$G$ has a subgroup of order $p^{n}$ .
Every $p$ -subgroup lies in a Sylow $p$ -subgroup, and all Sylow $p$ -subgroups are conjugate.
Their number $n_{p}$ satisfies $n_{p} \equiv 1 (mod p)$ and $n_{p} ∣ m$ .

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version