All Questions

It is well-known that there is an isomorphism between $PSp(4,3)$ (the symplectic group of dimension $4$ over $\mathbb F_3$) and $PSU(4,2^2)$ (the unitary group defined by $4\times4$ unitary matrices ...

I'm trying to understand the proof of Kantor's Singer cycle theorem, which asserts that if $G$ is a subgroup of $\operatorname{GL}(n,q)$ containing a Singer cycle then $\operatorname{GL}(n/s,q^s) \leq ...

An order-$m$ subplane of a finite projective plane of order $n$ is called a Baer subplane if $n=m^2$. It is known that the projective plane $PG(2,q)$ is a Baer subplane of the Desarguesian ...

Is the following statement true for finite reflection groups? Let $G$ be a finite reflection group acting on $\mathbb{R}^n$, let $x, y\in \mathbb{R}^n$ and let $z$ be in the orbit of $y$. If $\...

The only known finite projective plane with a transitive automorphism group is the Desarguesian plane $PG(2,q)$ and it seems likely that there are no others, although this is not (quite) proved. ...

Let $V$ be a vector space of finite dimentional $d$ over a field of prime order $p$. For what values of $d$ and $p$, one can find $d+1$ (pairwise distinct) hyperplanes (subspaces of dimension $d-1$) $...