ZEROS OF CHARACTERS ON PRIME ORDER ELEMENTS

Abstract

Suppose that G is a finite group, let χ be a faithful irreducible character of degree a power of p and let P be a Sylow p-subgroup of G. If χ(x) ≠ 0 for all elements of G of order p, then P is cyclic or generalized quaternion.

^* The research of the first author is supported by a grant of the Basque Government and by the University of the Basque Country UPV 127.310-EB160/98.

^† The second author is supported by DGICYT.

Acknowledgments

Notes

^* The research of the first author is supported by a grant of the Basque Government and by the University of the Basque Country UPV 127.310-EB160/98.

^† The second author is supported by DGICYT.