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Bias of group generators in finite and profinite groups: known results and open problems | ||
| International Journal of Group Theory | ||
| مقاله 6، دوره 4، شماره 2، شهریور 2015، صفحه 49-67 اصل مقاله (248.04 K) | ||
| نوع مقاله: Ischia Group Theory 2014 | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2015.9895 | ||
| نویسندگان | ||
| Eleonora Crestani؛ Andrea Lucchini* | ||
| Dipartimento di Matematica Universita; di Padova | ||
| چکیده | ||
| We analyze some properties of the distribution $Q_{G,k}$ of the first component in a $k$-tuple chosen uniformly in the set of all the $k$-tuples generating a finite group $G$ (the limiting distribution of the product replacement algorithm). In particular, we concentrate our attention on the study of the variation distance $\beta_k(G)$ between $Q_{G,k}$ and the uniform distribution. We review some known results, analyze several examples and propose some intriguing open questions. | ||
| کلیدواژه‌ها | ||
| Product replacement algorithm؛ profinite groups؛ group generators | ||
| مراجع | ||
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