On the polycirculant conjecture
| dc.creator | Golubchik, Aleksandr | |
| dc.date | 2002-04-16 | |
| dc.date | 2003-10-28 | |
| dc.date.accessioned | 2026-07-07T04:47:45Z | |
| dc.date.available | 2026-07-07T04:47:45Z | |
| dc.description | In the paper the foundation of the $k$-orbit theory is developed. The theory opens a new simple way to the investigation of groups and multidimensional symmetries. The relations between combinatorial symmetry properties of a $k$-orbit and its automorphism group are found. It is found the local property of a $k$-orbit. The difference between 2-closed group and $m$-closed group for $m>2$ is discovered. It is explained the specific property of Petersen graph automorphism group $n$-orbit. It is shown that any non-trivial primitive group contains a transitive imprimitive subgroup and as a result it is proved that the automorphism group of a vertex transitive graph (2-closed group) contains a regular element (polycirculant conjecture). Using methods of the $k$-orbit theory, it is considered different possibilities of permutation representation of a finite group and shown that the most informative, relative to describing of the structure of a finite group, is the permutation representation of the lowest degree. Using this representation it is obtained a simple proof of the W. Feit, J.G. Thompson theorem: Solvability of groups of odd order. It is described the enough simple structure of lowest degree representation of finite groups and found a way to constructing of the simple full invariant of a finite group. To the end, using methods of $k$-orbit theory, it is obtained one of possible polynomial solutions of the graph isomorphism problem. | |
| dc.description | 32 pages, Latex2e | |
| dc.identifier | https://arxiv.org/abs/math/0204209 | |
| dc.identifier | http://arxiv.org/abs/math/0204209 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63837 | |
| dc.subject | General Mathematics | |
| dc.subject | 20B05 (Primary) 05C25 (Secondary) | |
| dc.title | On the polycirculant conjecture | |
| dc.type | text |