**
Lecture notes for
Math 155: Designs and Groups
(Fall 1998)
**
If you find a mistake, omission, etc., please
let me know
by e-mail.

The orange balls
mark our current location in the course,
and the current problem set.

h0.ps:
introductory handout, showing different views of the
projective plane of order 2 (a.k.a. Fano plane)
and Petersen Graph [see also the background pattern for this page]
h1.ps:
*Ceci n'est pas un* Math 155 syllabus.

h2.ps:
Handout #2, containing
some basic definitions and facts about *finite fields*

h3.ps:
Handout #3, outlining
a proof of the simplicity of the finite groups
PSL_2(F) for |F|>4 and PSL_n(F) for n>2
(F a finite field, see Handout #2)

h4.ps:
Handout #4, using the existence and uniqueness
of the Steiner (3,4,8) system to prove that the
linear groups PSL_2(Z/7) and L_3(Z/2), both
simple (see Handout #3) and of order 168,
are isomorphic

h5.ps:
Handout #5, concerning the isomorphism between
the linear group L_4(Z/2) and the alternating
group A_8, both simple and of order 20160

h6.ps:
Handout #6, containing a sketch (to be filled-in
in class) of the existence and uniqueness of
the Moore graph of degree 7, a.k.a. the
*Hoffman-Singleton graph*. Can you deduce
the size of the automorphism group of this graph?

###
*****************************************************************

p1.ps:
First problem set, exploring the Fano plane (and generalizations)
and Petersen graph from the introductory handout.

p2.ps:
Second problem set, mostly on square designs and intersection
triangles.