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Universal deformation rings for the symmetric group S5 and one of its double covers
Journal article   Open access   Peer reviewed

Universal deformation rings for the symmetric group S5 and one of its double covers

Frauke M Bleher and Jennifer B Froelich
Journal of Pure and Applied Algebra, Vol.215(4), pp.523-530
2011
DOI: 10.1016/j.jpaa.2010.06.004
url
https://doi.org/10.1016/j.jpaa.2010.06.004View
Published (Version of record) Open Access

Abstract

Let S 5 denote the symmetric group on 5 letters, and let S ˆ 5 denote a non-trivial double cover of S 5 whose Sylow 2-subgroups are generalized quaternion groups. We determine the universal deformation rings R ( S 5 , V ) and R ( S ˆ 5 , V ) of each mod 2 representation V of S 5 that belongs to the principal 2-modular block of S 5 and whose stable endomorphism ring is given by scalars when it is inflated to S ˆ 5 . We show that for these V , a question raised by the first author and Chinburg concerning the relation of the universal deformation ring of V to the Sylow 2-subgroups of S 5 and S ˆ 5 , respectively, has an affirmative answer.

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