The cohomology rings of the special affine group of Fp^2 and of PSL(3,p)

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


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 =

Author: Long, Jane Holsapple

Source: University of Maryland

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