Small-diameter Cayley Graphs for Finite Simple Groups
نویسندگان
چکیده
Let 5 be a subset gener<lIing a fin ite group G. The corresponding Cayley gruph '§(G , 5 ) has the e lements of G as vertices ~od the. pairs 19. $g f. g E' G. $ E S . as edges. The diameter Q( ':!}(G , 5 ) is the smallL'lll iotcger d such thai every clement of G can be expressed as a word uf leoglh .,,;;. d using c lements (rom 5 U S ". A simple counl of words shows thai d ~ 10g~ I~ 1 (IG O. We prove Ihat Ihere is a constant C such Ihlll every nonabc lian finile simple group has ~ SCI S Ilf at most 7 gcncrato~ (or which the di3lncler of '8((;, S) i5 ~t mllst C lug l(il.
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عنوان ژورنال:
- Eur. J. Comb.
دوره 10 شماره
صفحات -
تاریخ انتشار 1989