University of IsfahanInternational Journal of Group Theory2251-76504220150601Bias of group generators in finite and profinite groups: known results and open problems4967989510.22108/ijgt.2015.9895ENEleonora CrestaniDipartimento di Matematica
Universita; di PadovaAndrea LucchiniDipartimento di Matematica
Universita; di PadovaJournal Article20141011We 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.http://ijgt.ui.ac.ir/article_9895_88e6083ca4021d45413514f530fff685.pdf