Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science (1990)

St. Louis, MO, USA

Oct. 22, 1990 to Oct. 24, 1990

ISBN: 0-8186-2082-X

pp: 857-865 vol.2

L. Babai , Chicago Univ., IL, USA

ABSTRACT

The diameter of a group G with respect to a set S of generators is the maximum over g in G of the length of the shortest word in S union S/sup -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 mod S mod is allowed to exceed (log mod G mod )/sup 1+c/(c>0), it plays a strong role when mod S mod =O(1).

INDEX TERMS

Rubik's-cube, finite groups, generators, communication networks

CITATION

L. Babai, A. Seress, A. Lubotzky, G. Hetyei and W. Kantor, "On the diameter of finite groups,"

*Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science(FOCS)*, St. Louis, MO, USA, 1990, pp. 857-865 vol.2.

doi:10.1109/FSCS.1990.89608

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