# Blocks with transitive fusion systems

Héthelyi, L., Kessar, R., Külshammer, B. & Sambale, B. (2015). Blocks with transitive fusion systems. Journal of Algebra, 424, pp. 190-207. doi: 10.1016/j.jalgebra.2014.10.042

 Preview
PDF - Accepted Version

## 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.

Item Type: Article 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 Block; Defect group; Fusion system Q Science > QA Mathematics School of Engineering & Mathematical Sciences > Department of Mathematical Science http://openaccess.city.ac.uk/id/eprint/6901