On groups with extremal blocks

Marcel Herzog*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)325-330
Number of pages6
JournalBulletin of the Australian Mathematical Society
Volume14
Issue number3
DOIs
StatePublished - Jun 1976
Externally publishedYes

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