Abstract
We obtain an upper bound for the dimension of the first cohomology group of a finite group acting faithfully and irreducibly on a finite dimensional module. We discuss the connection between results of this nature and generation questions for finite simple groups.
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Guralnick, R.M., Hoffman, C. (1998). The First Cohomology Group and Generation of Simple Groups. In: di Martino, L., Kantor, W.M., Lunardon, G., Pasini, A., Tamburini, M.C. (eds) Groups and Geometries. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8819-6_7
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DOI: https://doi.org/10.1007/978-3-0348-8819-6_7
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