arXiv subjects

Verena Möhler

Publications and source records attributed to Verena Möhler.

3 recordsLinked to original sources

arXiv2020

Parallelisms and Translations of (Affine) SL(2,q)-Unitals

Unitals can be obtained as closures of affine unitals via parallelisms. The isomorphism type of the closure depends on the chosen parallelism, which need not be unique. For affine $\operatorname{SL}(2,q)$-unitals, we introduce a class of parallelisms for odd order and one for square order. Translations are automorphisms of unitals, fixing each block through a given center. For each of the known parallelisms of affine $\operatorname{SL}(2,q)$-unitals, we compute all possible translations with centers on the block at infinity.

math.CO↗

arXiv2020

Three Affine SL(2,8)-Unitals

$\operatorname{SL}(2,q)$-unitals are unitals of order $q$ admitting a regular action of $\operatorname{SL}(2,q)$ on the complement of some block. We introduce three non-classical affine $\operatorname{SL}(2,8)$-unitals and their full automorphism groups. Each of those three affine unitals can be completed to at least two non-isomorphic unitals, leading to six pairwise non-isomorphic unitals of order $8$.

math.CO↗

arXiv2020

Automorphisms of (Affine) SL(2,q)-Unitals

$\operatorname{SL}(2,q)$-unitals are unitals of order $q$ admitting a regular action of $\operatorname{SL}(2,q)$ on the complement of some block. They can be obtained from affine $\operatorname{SL}(2,q)$-unitals via parallelisms. We compute a sharp upper bound for automorphism groups of affine $\operatorname{SL}(2,q)$-unitals and show that exactly two parallelisms are fixed by all automorphisms. In $\operatorname{SL}(2,q)$-unitals obtained as closures of affine $\operatorname{SL}(2,q)$-unitals via those two parallelisms, we show that there is one block fixed under the full automorphism group.

math.CO↗