The special affine group of Fp^2, p an odd prime, denoted Qd(p), plays an important role in the search for free actions by finite groups on products of spheres. The mod-p and integral** cohomology rings** of Qd(p) are computed and, as an extension of these results, the mod-p and p-primary part of the **integral cohomology**…

*Contents*

Introduction

0.1 Euler classes

0.2 The Steenrod Algebra

0.3 Effective Euler Classes

0.4 Other Constructions of Free Actions

0.5 Results

1 The Qd(p) Groups and Their **Cohomology**

1.1 Computation of H(Qd(p);Fp)

1.2 The Ring H(P;Fp)

1.3 The Map ResP H

1.4 Computation of Res−1(H(H;Fp)SL(2,p))

1.4.1 Computation of H(H;Fp)SL(2,p)

1.4.2 The Inverse Image of the Fixed Points Under Res

1.4.3 The Kernel of ReS

1.5 The Action of the Weyl Group

1.6 The Ring H(Qd(p);Fp)

1.7 The Rings H(Qd(p);Z) and H(Qd(p);Fq), q 6= p

1.8 The Case p = 3

1.9 The Restriction Maps from H(Qd(p);Fp)

1.9.1 The Case p = 3

2 The Cohomology of PSL(3, p)

2.1 Computation of Stable Elements

2.1.1 TheWeyl Groups of P and Qd(p) in PSL(3, p) and Their Induced Actions on Cohomology

2.1.2 Stability Under Elements of PSL(3, p) Which Do Not Normalize P

2.2 The Ring H(PSL(3, p);Fp)

2.3 The Integral Cohomology of PSL(3, p)

2.4 The Case p = 3

3 Depth and Dimension

3.0.1 The Case p =

Bibliography

Author: Long, Jane Holsapple

Source: University of Maryland

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