Determine order of a Sylow p-subgroup

Question

Let $G$ be a group of order $260$. For each prime $p$ dividing $|G|$, determine the order of a Sylow $p$-subgroup.

We have $|G| = 260 = 2^2 \cdot 5 \cdot 13$.

The order of a subgroup is its size. The question you have posted doesn't ask how many subgroups there are, or whether they are normal. — Mark Bennet, Mar 02 '14 at 21:39
Then I misinterpreted the question and I'll rework on it. But hypothetically, if the question did ask how many subgroups there are, how would I have done in answering that? — Cookie, Mar 02 '14 at 22:46
Note you can always have a single Sylow subgroup for a given prime (the cyclic group of order $260$ has just one subgroup of each order $r|260$) — Mark Bennet, Mar 02 '14 at 22:54

Cookie · Answer 1 · 2014-03-23T17:10:29.953

2

We have $|G| = 260 = 2^2 \cdot 5 \cdot 13$

So $G$ contains at least one of the following:

edited Mar 23 '14 at 17:10

answered Mar 23 '14 at 16:59

Cookie

Yes, but note you might want to say "At least one..." – Pedro Mar 23 '14 at 17:09

1 Answers1