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Normalizers of Primitive Permutation Groups
| Content Provider | Semantic Scholar |
|---|---|
| Author | Guralnick, Robert M. Maróti, Attila Pyber, L'aszl'o |
| Copyright Year | 2016 |
| Abstract | Let $G$ be a transitive normal subgroup of a permutation group $A$ of finite degree $n$. The factor group $A/G$ can be considered as a certain Galois group and one would like to bound its size. One of the results of the paper is that $|A/G| < n$ if $G$ is primitive unless $n = 3^{4}$, $5^4$, $3^8$, $5^8$, or $3^{16}$. This bound is sharp when $n$ is prime. In fact, when $G$ is primitive, $|\mathrm{Out}(G)| < n$ unless $G$ is a member of a given infinite sequence of primitive groups and $n$ is different from the previously listed integers. Many other results of this flavor are established not only for permutation groups but also for linear groups and Galois groups. |
| Starting Page | 1017 |
| Ending Page | 1063 |
| Page Count | 47 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/j.aim.2017.02.012 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1603.00187v2.pdf |
| Alternate Webpage(s) | http://real.mtak.hu/48131/1/1603.00187v2.pdf |
| Alternate Webpage(s) | https://doi.org/10.1016/j.aim.2017.02.012 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
