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On the diameter of finite groups

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5 Author(s)

The diameter of a group G with respect to a set S of generators is the maximum over g∈G of the length of the shortest word in SS-1 representing g. This concept arises in the contexts of efficient communication networks and Rubik's-cube-type puzzles. `Best' generators are pertinent to networks, whereas `worst' and `average' generators seem more adequate models for puzzles. A substantial body of recent work on these subjects by the authors is surveyed. Regarding the `best' case, it is shown that, although the structure of the group is essentially irrelevant if |S| is allowed to exceed (log|G |)1+c(c>0), it plays a strong role when |S|=O(1)

Published in:

Foundations of Computer Science, 1990. Proceedings., 31st Annual Symposium on

Date of Conference:

22-24 Oct 1990