Abstract
Let \({\mathfrak{A}}\) be a set of subgroups of the finite group G that form a central product M and such that G permutes the subgroups in \({\mathfrak{A}}\) by conjugation so that \({M\trianglelefteq G}\). (For example, \({\mathfrak{A}}\) could be the set of components of G). We show that the conjugation action of G on M can be “lifted” to an action of G on the direct product of the subgroups in \({\mathfrak{A}}\). Then we apply this procedure to obtain a Clifford theoretic reduction for an arbitrary p-block of G. Also we show that, in some cases, additional reductions can be applied.
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Harris, M.E. Central Products of Subgroups and Block Theory of Finite Groups. Results. Math. 67, 111–124 (2015). https://doi.org/10.1007/s00025-014-0397-z
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DOI: https://doi.org/10.1007/s00025-014-0397-z