Random Nilpotent Groups I
| Autor: | Yen Duong, Moon Duchin, Meng-Che Ho, Andrew P. Sánchez, Matthew Cordes |
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| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
General Mathematics media_common.quotation_subject 20F65 60G50 20D15 010102 general mathematics Group Theory (math.GR) 16. Peace & justice Infinity 01 natural sciences Random group Nilpotent 0103 physical sciences Free group FOS: Mathematics 010307 mathematical physics 0101 mathematics Nilpotent group Mathematics - Group Theory Quotient Standard model (cryptography) Mathematics media_common |
| Zdroj: | International Mathematics Research Notices. 2018:1921-1953 |
| ISSN: | 1687-0247 1073-7928 |
| DOI: | 10.1093/imrn/rnv370 |
| Popis: | We study random nilpotent groups in the well-established style of random groups, by choosing relators uniformly among freely reduced words of (nearly) equal length and letting the length tend to infinity. Whereas random groups are quotients of a free group by such a random set of relators, random nilpotent groups are formed as corresponding quotients of a free nilpotent group. This model reveals new phenomena because nilpotent groups are not "visible" in the standard model of random groups (due to the sharp phase transition from infinite hyperbolic to trivial groups). Comment: Version 3 contains an addition of an appendix filling in details for some arithmetic properties of random walks as well as other small edits |
| Databáze: | OpenAIRE |
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