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On characters in the principal 2-block

Published online by Cambridge University Press:  09 April 2009

Thomas R. Berger  and
Marcel Herzog
Thomas R. Berger
Affiliation:
Department of Mathematics, Institute of Advanced Studies, The Australian National University, Canberra, ACT 2600.
Marcel Herzog
Affiliation:
Department of Mathematics, Institute of Advanced Studies, The Australian National University, Canberra, ACT 2600.
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Abstract

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Let k be a complex number and let u be an element of a finite group G. Suppose that u does not belong to O(G), the maximal normal subgroup of G of odd order. It is shown that G satisfies X(1) – X(u) = k for every complex nonprincipal irreducible character X in the principal 2-block of G if and only if G/O(G) is isomorphic either to C2, a cyclic group of order 2, or to PSL (2, 2n), n ≧ 2.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 3 , May 1978 , pp. 264 - 268
Copyright
Copyright © Australian Mathematical Society 1978

References

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