Abstract

Suppose that all nontrivial subsections of a $p$-block $B$ are conjugate (where $p$ is a prime). By using the classification of the finite simple groups, we prove that the defect groups of $B$ are either extraspecial of order $p^3$ with $p \in \{3,5\}$ or elementary abelian.

Publication Type:	Article
Additional Information:	NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Algebra. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Algebra, Vol.424 (2015) 10.1016/j.jalgebra.2014.10.042
Publisher Keywords:	Block; Defect group; Fusion system
Subjects:	Q Science > QA Mathematics
Departments:	School of Mathematics, Computer Science & Engineering > Mathematics

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