any maths geeks out there?

[ajva]

Erm...

I am right in thinking, am I not, that a group of order 1722 can have only one Sylow 7-subgroup? Or have I missed something?

It's just that the next bit tells me to use a counting argument to show that if it has more than one then it can have only one Sylow 41-subgroup. It seems like the second question is supposed to be theoretical but I just wanted to make sure. :o(

Any comments welcome, although I don't expect I'm going to be snowed under with responses.

Comments

[ciphergoth.livejournal.com]

But there isn't a value which satisfies both of these except 1 (or is there???)

Yes there is: 246 = 1 (mod 7).

D'oh! (A Homer Simpson moment)

[ajva.livejournal.com]

Bingo!

Cheers Paul. ;o)

Also, it makes the next question a piece of piss.

A. x