Lifting graph automorphisms along solvable regular covers
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2012
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| _version_ | 1866910342066470912 |
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| author | Chen, Haimiao Kwak, Jin Ho |
| author_facet | Chen, Haimiao Kwak, Jin Ho |
| contents | A {\em solvable} cover of a graph is a regular cover whose covering transformation group is solvable. In this paper, we show that a solvable cover of a graph can be decomposed into layers of abelian covers, and also, a lift of a given automorphism of the base graph of a solvable cover can be decomposed into layers of lifts of the automorphism in the layers of the abelian covers. This procedure is applied to classify metacyclic covers of the tetrahedron branched at face-centers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1209_4283 |
| institution | arXiv |
| publishDate | 2012 |
| record_format | arxiv |
| spellingShingle | Lifting graph automorphisms along solvable regular covers Chen, Haimiao Kwak, Jin Ho Geometric Topology 05C10, 05C25, 20B25 A {\em solvable} cover of a graph is a regular cover whose covering transformation group is solvable. In this paper, we show that a solvable cover of a graph can be decomposed into layers of abelian covers, and also, a lift of a given automorphism of the base graph of a solvable cover can be decomposed into layers of lifts of the automorphism in the layers of the abelian covers. This procedure is applied to classify metacyclic covers of the tetrahedron branched at face-centers. |
| title | Lifting graph automorphisms along solvable regular covers |
| topic | Geometric Topology 05C10, 05C25, 20B25 |
| url | https://arxiv.org/abs/1209.4283 |