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On characters in the principal 2-block, II

Published online by Cambridge University Press:  09 April 2009

Marcel Herzog  and
Cheryl E. Praeger
Marcel Herzog
Affiliation:
Department of Mathematics Institute of Advanced StudiesThe Australian National University Canberra, Australia2600 and Department of MathematicsTel-Aviv UniversityTel-Aviv, Israel
Cheryl E. Praeger
Affiliation:
Department of Mathematics University of Wrstern AustraliaNedlands, Australia6009
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Abstract

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Let k be a non-zero complex number and let u and v be elements of a finite group G. Suppose that at most one of u and v belongs to O(G), the maximal normal subgroup of G of odd order. It is shown that G satisfies X(v)–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 to one of the following groups: C2, PSL(2, 2n) or pΣL(2, 52a+1), where n≥2 and a ≥ 1.

Subject classification (Amer. Math. Soc. (MOS) 1970): 20 C 20

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 1 , August 1979 , pp. 100 - 106
Copyright
Copyright © Australian Mathematical Society 1979

References

Berger, Thomas R. and Herzog, Marcel (1978), ‘On characters in the principal 2-block’, J. Austral. Math. Soc, (Ser. A) 25, 264–268.CrossRefGoogle Scholar
Isaacs, I. Martin (1976), Character theory of finite groups (Academic Press, New York, San Francisco and London).Google Scholar
Ward, Harold N. (1966), ‘On Ree's series of simple groups’, Trans. Amer. Math. Soc. 121, 62–89.Google Scholar