Please use this identifier to cite or link to this item: http://dx.doi.org/10.18419/opus-11527
Authors: Nitsche, Sebastian
Title: The minimal projective resolution of Z_(2) over Z_(2)S_4
Issue Date: 2017
metadata.ubs.publikation.typ: Abschlussarbeit (Master)
metadata.ubs.publikation.seiten: 106
URI: http://elib.uni-stuttgart.de/handle/11682/11544
http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-115448
http://dx.doi.org/10.18419/opus-11527
Abstract: We consider the trivial module Z_(2) over the group ring Z_(2)S_4. Using the Wedderburn image of Z_(2)S_4, a minimal projective resolution of Z_(2) over Z_(2)S_4 with regular behavior is constructed. We give a closed formula for the projective terms and the differentials. The minimal projective resolution is used to calculate the cohomology groups of S_4 over Z_(2). In 1974, Thomas gave a description of the cohomology ring of S_4 as a factor ring of a polynomial ring. As far as we were able to compare both using Magma, our calculation is in accordance with his result.
Appears in Collections:08 Fakultät Mathematik und Physik

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