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On groups with extremal blocks
Published online by Cambridge University Press: 17 April 2009
Abstract
Let G be a finite group. It is shown that G is 2-closed if and only if
(a) every 2-block of G has full defect, and
(b) every Sylow 2-intersection is centralized by a Sylow 2-subgroup of G.
As a consequence it is shown that G is a TI-group if and only if every 2-block of G has either full defect or defect zero and (b) holds. This result and a theorem of Kwok yield complete characterizations of finite groups with certain relations being satisfied by every nonprincipal irreducible character.
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- Copyright © Australian Mathematical Society 1976
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