×

Numerical characteristics of groups and the relations between them. (English. Russian original) Zbl 0996.20057

J. Math. Sci., New York 107, No. 5, 4147-4157 (2001); translation from Zap. Nauchn. Semin. POMI 256, 5-18 (1999).
Summary: The entropy of a random walk on a discrete countable group can be used for comparison of systems of generators. A fundamental inequality between growth, entropy and escape rate gives the possibility to define “the best” system of generators. We formulate a new circle of problems related to growth and other asymptotic characteristics of groups.

MSC:

20P05 Probabilistic methods in group theory
20F05 Generators, relations, and presentations of groups
60G50 Sums of independent random variables; random walks
20F69 Asymptotic properties of groups
28D20 Entropy and other invariants
60B15 Probability measures on groups or semigroups, Fourier transforms, factorization
PDFBibTeX XMLCite
Full Text: DOI