| Title: | Semiregular automorphisms in vertex-transitive graphs with a solvable group of automorphisms |
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| Authors: | ID Marušič, Dragan (Author) |
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| Files: |  RAZ_Marusic_Dragan_i2017.pdf (235,26 KB)
MD5: 735FBD4E5D327BA888FB5876F88AC383
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| Language: | English |
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| Work type: | Unknown |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| Abstract: | It has been conjectured that automorphism groups of vertex-transitive (di)graphs, and more generally 2-closures of transitive permutation groups, must necessarily possess a fixed-point-free element of prime order, and thus a non-identity element with all orbits of the same length, in other words, a semiregular element. The known affirmative answers for graphs with primitive and quasiprimitive groups of automorphisms suggest that solvable groups need to be considered if one is to hope for a complete solution of this conjecture. It is the purpose of this paper to present an overview of known results and suggest possible further lines of research towards a complete solution of the problem. |
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| Keywords: | solvable group, semiregular automorphism, fixed-point-free automorphism, polycirculant conjecture |
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| Year of publishing: | 2017 |
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| Number of pages: | str. 461-468 |
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| Numbering: | Vol. 13, no. 2 |
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| PID: | 20.500.12556/RUP-17629  |
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| UDC: | 519.17:512.54 |
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| ISSN on article: | 1855-3966 |
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| COBISS.SI-ID: | 1539752900 |
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| Publication date in RUP: | 03.01.2022 |
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| Views: | 891 |
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| Downloads: | 17 |
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