Crestani, E., Lucchini, A. (2015). Bias of group generators in finite and profinite groups: known results and open problems. International Journal of Group Theory, 4(2), 49-67. doi: 10.22108/ijgt.2015.9895

Eleonora Crestani; Andrea Lucchini. "Bias of group generators in finite and profinite groups: known results and open problems". International Journal of Group Theory, 4, 2, 2015, 49-67. doi: 10.22108/ijgt.2015.9895

Crestani, E., Lucchini, A. (2015). 'Bias of group generators in finite and profinite groups: known results and open problems', International Journal of Group Theory, 4(2), pp. 49-67. doi: 10.22108/ijgt.2015.9895

Crestani, E., Lucchini, A. Bias of group generators in finite and profinite groups: known results and open problems. International Journal of Group Theory, 2015; 4(2): 49-67. doi: 10.22108/ijgt.2015.9895

Bias of group generators in finite and profinite groups: known results and open problems

^{}Dipartimento di Matematica Universita; di Padova

Abstract

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.

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