Geodesic
The Farrell cohomology of SP (𝑝−1, ℤ)
Documenta mathematica, Tome 7 (2002), pp. 239-254
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Let p be an odd prime with odd relative class number h−. In this article we compute the Farrell cohomology of Sp(p−1,Z), the first p-rank one case. This allows us to determine the p-period of the Farrell cohomology of Sp(p−1,Z), which is 2y, where p−1=2ry,y odd. The p-primary part of the Farrell cohomology of Sp(p−1,Z) is given by the Farrell cohomology of the normalizers of the subgroups of order p in Sp(p−1,Z). We use the fact that for odd primes p with h− odd a relation exists between representations of Z/pZ in Sp(p−1,Z) and some representations of Z/pZ in U((p−1)/2).
DOI : 10.4171/dm/126
Classification : 20G10
Mots-clés : cohomology theory 
@article{10_4171_dm_126,
     author = {Cornelia Busch},
     title = {The {Farrell} cohomology of {SP} (\ensuremath{\mathit{p}}\ensuremath{-}1, {\ensuremath{\mathbb{Z}})}},
     journal = {Documenta mathematica},
     pages = {239--254},
     year = {2002},
     volume = {7},
     doi = {10.4171/dm/126},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/126/}
}
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Cornelia Busch. The Farrell cohomology of SP (𝑝−1, ℤ). Documenta mathematica, Tome 7 (2002), pp. 239-254. doi: 10.4171/dm/126

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