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.