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Sectional split extensions arising from lifts of groupsPožar, Rok, 1986-Krovne tehnike so se izkazale kot učinkovito orodje pri klasifikaciji več neskončnih družin povezanih simetričnih grafov. Ena izmed pogostih tehnik, s katerimi se srečamo, temelji na konceptu dviga ... avtomorfizmov grup vzdolž regularnih krovnih projekcij ▫$\wp \colon \tilde{X} \to X$▫. Učinkovite računske metode so znane v primeru regulanih krovov s ciklično ali elementarno abelsko grupo krovnih transformacij CT▫$(\wp)$▫. V članku študiramo problem dviga pri dodatnem pogoju, kako naj se grupa dvigne: za dani povezan graf▫ $X$▫ in podgrupo ▫$G$▫ njegovih avtomorfizmov poišči vse povezane regularne krovne projekcije ▫$\wp \colon \tilde{X} \to X$▫, vzdolž katerih se ▫$G$▫ dvigne kot sekcijska razcepna razširitev. To pomeni, da obstajakomplement ▫$\overline{G}$▫ k CT▫$(\wp)$▫ znotraj dvignjene grupe ▫$\tilde{G}$▫, tako da ima ▫$\overline{G}$▫ orbito, ki seka vsako vlakno v največ enem vozlišču. Za ilustracijo konstruiramo vse povezane elementarno ableske regularne krove polnega grafa ▫$K_4$▫, vzdolž katerih se ciklična grupa reda 4 dvigne kot sekcijska razcepna razširitev.Source: Ars mathematica contemporanea. - ISSN 1855-3966 (Vol. 6, no. 2, 2013, str. 393-408)Type of material - article, component part ; adult, seriousPublish date - 2013Language - englishCOBISS.SI-ID - 1024540756
Author
Požar, Rok, 1986-
Topics
covering projection |
graph |
group extension |
lifting automorphisms |
voltage assignment
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Požar, Rok, 1986- | 32026 |
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