Where can I find information on the relationship between group theory generators and random number generators?

Where can I find information on the relationship between group theory generators and random number generators?

Can the behavior of group generators be related to the behavior of random number generators It may be coincidence, but in Donald Knuths Art of Programming Volume 2 on seminumerical algorithms, he uses notation similar to leftg right, the notation used for the subgroup generated by g, when describing a random sequence. When is the sequence of generated elements random

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