| Title:
|
Extremely primitive groups and linear spaces (English) |
| Author:
|
Guan, Haiyan |
| Author:
|
Zhou, Shenglin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
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1572-9141 (online) |
| Volume:
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66 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
445-455 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A non-regular primitive permutation group is called extremely primitive if a point stabilizer acts primitively on each of its nontrivial orbits. Let $\mathcal S$ be a nontrivial finite regular linear space and $G\leq {\rm Aut}(\mathcal S).$ Suppose that $G$ is extremely primitive on points and let rank$(G)$ be the rank of $G$ on points. We prove that rank$(G)\geq 4$ with few exceptions. Moreover, we show that ${\rm Soc}(G)$ is neither a sporadic group nor an alternating group, and $G={\rm PSL}(2,q)$ with $q+1$ a Fermat prime if ${\rm Soc}(G)$ is a finite classical simple group. (English) |
| Keyword:
|
linear space |
| Keyword:
|
automorphism |
| Keyword:
|
point-primitive automorphism group |
| Keyword:
|
extremely primitive permutation group |
| MSC:
|
05B05 |
| MSC:
|
05B25 |
| MSC:
|
20B15 |
| MSC:
|
20B25 |
| idZBL:
|
Zbl 06604478 |
| idMR:
|
MR3519613 |
| DOI:
|
10.1007/s10587-016-0267-9 |
| . |
| Date available:
|
2016-06-16T12:53:28Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145735 |
| . |
| Reference:
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