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370:{\displaystyle \operatorname {diam} (G)\leqslant \left(\log |G|\right)^{{\mathcal {O}}(1)}.}
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Many partial results are known but the full conjecture remains open.
478:
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235:, the Cayley graph for a generating set with one generator is an
464:; Seress, Ákos (2014), "On the diameter of permutation groups",
400:; Seress, Ákos (1992), "On the diameter of permutation groups",
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243:. The diameter of this graph, and of the group, is
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280:It is conjectured, for all non-abelian finite
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447:, Conj. 1.7. This conjecture is misquoted by
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150:{\displaystyle \Lambda =\left(G,S\right)}
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451:, who omit the non-abelian qualifier.
186:{\displaystyle \left(G,\circ \right)}
67:{\displaystyle \left(G,\circ \right)}
7:
511:
509:
270:{\displaystyle \lfloor s/2\rfloor }
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14:
402:European Journal of Combinatorics
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35:is a measure of its complexity.
220:taken over all generating sets
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1:
424:10.1016/S0195-6698(05)80029-0
529:. You can help Knowledge by
449:Helfgott & Seress (2014)
488:10.4007/annals.2014.179.2.4
227:For instance, every finite
602:
508:
445:Babai & Seress (1992)
193:is the largest value of
157:. Then the diameter of
38:Consider a finite group
16:Concept in group theory
581:Measures of complexity
525:-related article is a
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466:Annals of Mathematics
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213:{\displaystyle D_{S}}
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101:{\displaystyle D_{S}}
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462:Helfgott, Harald A.
586:Group theory stubs
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468:, Second Series,
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229:cyclic group
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25:group theory
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241:cycle graph
570:Categories
384:References
108:to be the
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415:1109.3550
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176:∘
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