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Barcelona Algebraic Topology Group
Friday's Topology Seminar 2018-19 PDF Print E-mail
Written by Natàlia Castellana Vila   
Friday, 30 November 2018 14:12

Speaker: Matthew Gelvin (Bilkent University, Ankara)
Title:Fusion-minimal groups
Place:
Room Seminar C3b
Date: Friday April 27, 12h-13h

Abstract: Every saturated fusion system $\mathcal{F}$ on the $p$-group $S$ has an associated collection of characteristic bisets.  These are $(S,S)$-bisets that determine $\mathcal{F}$, and are in turn determined by $\mathcal{F}$ up to a more-or-less explicit parameterization.  In particular, there is always a unique minimal $\mathcal{F}$-characteristic biset, $\Omega_\mathcal{F}$. If $G$ is a finite group containing $S$ as a Sylow $p$-subgroup and realizing $\mathcal{F}$, then $G$ is itself, when viewed as an $(S,S)$-biset, $\mathcal{F}$-characteristic.  If it happens that $_SG_S=\Omega_\mathcal{F}$ is the minimal biset for its fusion system, we say that $G$ is \emph{fusion-minimal}.

In joint work with Sune Reeh, it was shown that any strictly $p$-constrained group (i.e., one that satisfies $C_G(O_p(G))\leq O_p(G)$) is fusion minimal.  We conjecture that converse implication holds.  In this talk, based on joint work with Justin Lynd, we prove this to be the case when $p$ is odd and describe the obstruction to a complete proof.  Along the way, we will draw a connection with the module structure of block algebras and how this relates to the question at hand.

See the calendar for upcoming events.

Last Updated on Tuesday, 23 April 2019 13:11
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This is the web site of the Algebraic Topology Team in Barcelona (Grup de Topologia Algebraica de Barcelona, 2014SGR-42 and Homotopy theory of algebraic structures, MTM2016-80439-P).

Our research interests include a variety of subjects in algebraic topology, group theory, homological algebra, and category theory. Here you will find information about us and our common activities.

 

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