What is F_n?

[Julian Benali]

I was using lmfdb.org and I came across the group “F_9”. I also saw an F_8 and F_7. So I wondered what F_n is supposed to be. I wasn’t listed as one of the support families. Clicking on the link for F_9, F_8, or F_7 also didn’t give a name. These are finite groups, so they’re not free groups like I would expect F_n to represent. So what is lmfdb.org referring to when it uses the notation F_n? Is there some source for this?

Julian Benali

[John Jones]

Hi,

The F stands for Frobenius.  This is a family all of whose members are examples of Frobenius groups.  In the knowl for family https://beta.lmfdb.org/knowledge/show/group.families it is listed there.  Clicking on Frobenius gives their full definition.

You say there was a spot where group families are explained, but this one is missing.  Let us know where that is and we will fix it.

John Jones

On Fri, Oct 3, 2025 at 6:51 AM Julian Benali <julian...@gmail.com> wrote:

I was using lmfdb.org and I came across the group “F_9”. I also saw an F_8 and F_7. So I wondered what F_n is supposed to be. I wasn’t listed as one of the support families. Clicking on the link for F_9, F_8, or F_7 also didn’t give a name. These are finite groups, so they’re not free groups like I would expect F_n to represent. So what is lmfdb.org referring to when it uses the notation F_n? Is there some source for this?

Julian Benali

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