Sylow Numbers from Character Tables and Integral Group Rings
نویسندگان
چکیده
G. Navarro raised the question whether the ordinary character table X(G) of a finite group G determines the Sylow numbers of G. In this note we show that this is the case when G is nilpotent-by-nilpotent, quasinilpotent, Frobenius group or a 2-Frobenius group. In particular Sylow numbers of supersoluble groups are determined by their ordinary character table. If G and H are finite groups with isomorphic integral group rings then it is well known that X(G) and X(H) coincide. In the last part of this note we show that the integral group ring ZG determines the number of Sylow q-subgroups provided G is q-contrained. It follows that ZG determines the Sylow numbers of G provided G is soluble.
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