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Elementary Proofs of some Results on Representations of p-groups

M.A. Shokrollahi
TR-95-054 September 1995

Abstract A result of Roquette [3] states that if D is an absolutely irreducible representation of a p-group G over the field of complex numbers, then D can be realized in K((g) j g 2 G), where is the character of D and K = Q or K = Q(i) according to whether p 6= 2 or p = 2. Based on Baum and Clausen's [1] algorithm for computing the irreducible representations of supersolvable groups, we give an elementary proof of a theorem which, among other well-known facts on representations of p-groups, implies Roquette's result.