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p. A closed subset H of G is
called p-valenced if each element of H is
p-valenced. It is called a p-subset if it
p-valenced and n is a power of _{H}p.
It is called a Sylow p-subset if p does not divide
n. Let us write _{G}/n_{H}Syl
in order to denote the set of all Sylow _{p}(G)p-subsets of G.
In my talk, I will prove that, if G is p-valenced,
p divides |Syl|_{p}(G)-1,
thereby generalizing Sylow's well-known theorems on finite
groups.Reference: A generalization of Sylow's theorems on
finite groups to association schemes. |

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