Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-05T14:17:14.917Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

Roger, W. Carter (1972), Simple Groups of Lie Type (John Wiley, New York).Google Scholar
Marcel, Herzog (1976), ‘On groups with extremal blocks’, Bull. Austral. Math. Soc. 14, 325–330.Google Scholar
Marcel, Herzog (to appear), ‘On linear relations between character values’, J. Algebra.Google Scholar
Zvonimir, Janko (1966), ‘A new finite simple group with abelian Sylow 2-subgroups and its characterization’, J. Algebra 3, 147–186.Google Scholar
Chung-Mo, Kwok (1975), ‘A characterization of PSL(2, 2m), J. Algebra 34, 288–291.Google Scholar
John, H. Walter (1969), ‘The characterization of finite groups with abelian Sylow 2-subgroups’, Ann. of Math. (2) 89, 405–514.Google Scholar
Harold, N. Ward (1966), ‘On Ree's series of simple groups’, Trans. Amer. Math. Soc. 121, 62–89.Google Scholar