From: mareg@mimosa.csv.warwick.ac.uk ()
Subject: Re: PSL_3(2)
Date: Sun, 28 Oct 2001 16:30:35 +0000 (UTC)
Newsgroups: sci.math
Summary: The several simple groups of order 20160

In article <f6f470cf7123262ee60a5ac97abcbc61.22128@mygate.mailgate.org>,
	"Robin Chapman" <rjc@maths.ex.ac.uk> writes:
>
>When you say PSL_3(2), do you actually mean PSL_3(4) - that
>well known example of a simple group with the same order
>as A_8 but not isomorphic to it?

What is remarkable is that PSL_4(2) also has order 20160.
But of course this is isomorphic to one of PSL_3(4) and A_8.

Here is a problem (or rather 2 problems) to help pass the time on Sunday:

1. Which one is it?
2. Find a nice proof of the relevant isomorphism.

I know the answer to 1 of course, and I have the feeling I once knew
an answer to 2, but I cannot remember it now.

Derek Holt.