A semifield plane of odd order admitting an autotopism subgroup isomorphic to \(A_5\) (Q721373)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A semifield plane of odd order admitting an autotopism subgroup isomorphic to \(A_5\) |
scientific article; zbMATH DE number 6908380
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A semifield plane of odd order admitting an autotopism subgroup isomorphic to \(A_5\) |
scientific article; zbMATH DE number 6908380 |
Statements
A semifield plane of odd order admitting an autotopism subgroup isomorphic to \(A_5\) (English)
0 references
19 July 2018
0 references
Consider a semifield plane \(\pi\) of order \(p^{N}\), \(p>2\) a prime. The authors prove: If the autotopism group of \(\pi\) contains \(A_{5}\), and is in particular non solvable, then \(N=4n\) and the matrices describing spread sets that defines \(\pi\) have a special form described in the paper. If \(p\equiv 1\pmod 4\), then this cannot happen. The authors use elaborate calculations with matrices inside the spread sets.
0 references
semifield plane
0 references
collineation group
0 references
alternating group
0 references
spread set
0 references
0 references
