تقرير
Finiteness of outer automorphism groups of random right-angled Artin groups
| العنوان: | Finiteness of outer automorphism groups of random right-angled Artin groups |
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| المؤلفون: | Day, Matthew B. |
| المصدر: | Algebr. Geom. Topol. 12 (2012) 1553-1583 |
| سنة النشر: | 2011 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Group Theory, 20F05, 20F28, 05C80 |
| الوصف: | We consider the outer automorphism group Out(A_Gamma) of the right-angled Artin group A_Gamma of a random graph Gamma on n vertices in the Erdos--Renyi model. We show that the functions (log(n)+log(log(n)))/n and 1-(log(n)+log(log(n)))/n bound the range of edge probability functions for which Out(A_Gamma) is finite: if the probability of an edge in Gamma is strictly between these functions as n grows, then asymptotically Out(A_Gamma) is almost surely finite, and if the edge probability is strictly outside of both of these functions, then asymptotically Out(A_Gamma) is almost surely infinite. This sharpens results of Ruth Charney and Michael Farber from their preprint "Random groups arising as graph products", arXiv:1006.3378v1. Comment: 29 pages. Mostly rewritten, results tightened, statements corrected, gaps filled |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.2140/agt.2012.12.1553 |
| URL الوصول: | http://arxiv.org/abs/1103.0479 |
| رقم الأكسشن: | edsarx.1103.0479 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.2140/agt.2012.12.1553 |
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