Eliminating components in Quillen's Conjecture
| Autor: | Piterman, Kevin I., Smith, Stephen D. |
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| Rok vydání: | 2020 |
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| Druh dokumentu: | Working Paper |
| Popis: | We generalize an earlier result of Segev, which shows that {\em some\/} component in a minimal counterexample to Quillen's conjecture must admit an outer automorphism. We show in fact that {\em every\/} component must admit an outer automorphism. Thus we transform his restriction-result on components to an elimination-result: namely one which excludes any component which does not admit an outer automorphism. Indeed we show that the outer automorphisms admitted must include $p$-outers: that is, outer automorphisms of order divisible by $p$. This gives stronger, concrete eliminations: for example if $p$ is odd, it eliminates sporadic and alternating components -- thus reducing to Lie-type components (and typically forcing $p$-outers of field type). For $p = 2$, we obtain similar but less restrictive results. We also provide some tools to help eliminate suitable components that do admit $p$-outers in a minimal counterexample. Comment: 37 pages, comments are welcome |
| Databáze: | arXiv |
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