University of Isfahan International Journal of Group Theory 2251-7650 4 2 2015 06 01 Bias of group generators in finite and profinite groups: known results and open problems 49 67 9895 10.22108/ijgt.2015.9895 EN Eleonora Crestani Dipartimento di Matematica Universita; di Padova Andrea Lucchini Dipartimento di Matematica Universita; di Padova Journal Article 2014 10 11 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. Product replacement algorithm profinite groups group generators https://ijgt.ui.ac.ir/article_9895_88e6083ca4021d45413514f530fff685.pdf